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Exam 4: Quadrilaterals

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Exam 1: Line and Angle Relationships13 Questionsadd course
Exam 2: Parallel Lines13 Questionsadd course
Exam 3: Triangles16 Questionsadd course
Exam 4: Quadrilaterals14 Questionsadd course
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Exam 12: Geometry Problems: Complementary Angles, Collinear Points, and Similar Triangles916 Questionsadd course
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-In quadrilateral ABCD, the midpoints of the sides are joined in order. Use the auxiliary diagonals to explain why the resulting quadrilateral MNPQ must be a parallelogram. -In quadrilateral ABCD, the midpoints of the sides are joined in order. Use the auxiliary diagonals to explain why the resulting quadrilateral MNPQ must be a parallelogram.

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The line segements that join midpoints of 2 sides of a triangle are parallel to the third side of the triangle. For this reason, The line segements that join midpoints of 2 sides of a triangle are parallel to the third side of the triangle. For this reason, in and in ; thus, it follows that . Similarly, in and in ; thus, . By definition, it follows that MNPQ is a parallelogram. in The line segements that join midpoints of 2 sides of a triangle are parallel to the third side of the triangle. For this reason, in and in ; thus, it follows that . Similarly, in and in ; thus, . By definition, it follows that MNPQ is a parallelogram. and The line segements that join midpoints of 2 sides of a triangle are parallel to the third side of the triangle. For this reason, in and in ; thus, it follows that . Similarly, in and in ; thus, . By definition, it follows that MNPQ is a parallelogram. in The line segements that join midpoints of 2 sides of a triangle are parallel to the third side of the triangle. For this reason, in and in ; thus, it follows that . Similarly, in and in ; thus, . By definition, it follows that MNPQ is a parallelogram. ; thus, it follows
that The line segements that join midpoints of 2 sides of a triangle are parallel to the third side of the triangle. For this reason, in and in ; thus, it follows that . Similarly, in and in ; thus, . By definition, it follows that MNPQ is a parallelogram. . Similarly, The line segements that join midpoints of 2 sides of a triangle are parallel to the third side of the triangle. For this reason, in and in ; thus, it follows that . Similarly, in and in ; thus, . By definition, it follows that MNPQ is a parallelogram. in The line segements that join midpoints of 2 sides of a triangle are parallel to the third side of the triangle. For this reason, in and in ; thus, it follows that . Similarly, in and in ; thus, . By definition, it follows that MNPQ is a parallelogram. and The line segements that join midpoints of 2 sides of a triangle are parallel to the third side of the triangle. For this reason, in and in ; thus, it follows that . Similarly, in and in ; thus, . By definition, it follows that MNPQ is a parallelogram. in The line segements that join midpoints of 2 sides of a triangle are parallel to the third side of the triangle. For this reason, in and in ; thus, it follows that . Similarly, in and in ; thus, . By definition, it follows that MNPQ is a parallelogram. ; thus, The line segements that join midpoints of 2 sides of a triangle are parallel to the third side of the triangle. For this reason, in and in ; thus, it follows that . Similarly, in and in ; thus, . By definition, it follows that MNPQ is a parallelogram. .
By definition, it follows that MNPQ is a parallelogram.

-Provide missing reasons for the proof of the theorem, A diagonal of a parallelogram separates it into two congruent triangles. Given: with diagonal Prove: S1. with diagonal R1. S2. R2. S3. R3. S4. R4. S5. R5. S6. R6. S7. R7. -Provide missing reasons for the proof of the theorem, "A diagonal of a parallelogram separates it into two congruent triangles." Given: -Provide missing reasons for the proof of the theorem, A diagonal of a parallelogram separates it into two congruent triangles. Given: with diagonal Prove: S1. with diagonal R1. S2. R2. S3. R3. S4. R4. S5. R5. S6. R6. S7. R7. with diagonal -Provide missing reasons for the proof of the theorem, A diagonal of a parallelogram separates it into two congruent triangles. Given: with diagonal Prove: S1. with diagonal R1. S2. R2. S3. R3. S4. R4. S5. R5. S6. R6. S7. R7. Prove: -Provide missing reasons for the proof of the theorem, A diagonal of a parallelogram separates it into two congruent triangles. Given: with diagonal Prove: S1. with diagonal R1. S2. R2. S3. R3. S4. R4. S5. R5. S6. R6. S7. R7. S1. -Provide missing reasons for the proof of the theorem, A diagonal of a parallelogram separates it into two congruent triangles. Given: with diagonal Prove: S1. with diagonal R1. S2. R2. S3. R3. S4. R4. S5. R5. S6. R6. S7. R7. with diagonal -Provide missing reasons for the proof of the theorem, A diagonal of a parallelogram separates it into two congruent triangles. Given: with diagonal Prove: S1. with diagonal R1. S2. R2. S3. R3. S4. R4. S5. R5. S6. R6. S7. R7. R1. S2. -Provide missing reasons for the proof of the theorem, A diagonal of a parallelogram separates it into two congruent triangles. Given: with diagonal Prove: S1. with diagonal R1. S2. R2. S3. R3. S4. R4. S5. R5. S6. R6. S7. R7. R2. S3. -Provide missing reasons for the proof of the theorem, A diagonal of a parallelogram separates it into two congruent triangles. Given: with diagonal Prove: S1. with diagonal R1. S2. R2. S3. R3. S4. R4. S5. R5. S6. R6. S7. R7. R3. S4. -Provide missing reasons for the proof of the theorem, A diagonal of a parallelogram separates it into two congruent triangles. Given: with diagonal Prove: S1. with diagonal R1. S2. R2. S3. R3. S4. R4. S5. R5. S6. R6. S7. R7. R4. S5. -Provide missing reasons for the proof of the theorem, A diagonal of a parallelogram separates it into two congruent triangles. Given: with diagonal Prove: S1. with diagonal R1. S2. R2. S3. R3. S4. R4. S5. R5. S6. R6. S7. R7. R5. S6. -Provide missing reasons for the proof of the theorem, A diagonal of a parallelogram separates it into two congruent triangles. Given: with diagonal Prove: S1. with diagonal R1. S2. R2. S3. R3. S4. R4. S5. R5. S6. R6. S7. R7. R6. S7. -Provide missing reasons for the proof of the theorem, A diagonal of a parallelogram separates it into two congruent triangles. Given: with diagonal Prove: S1. with diagonal R1. S2. R2. S3. R3. S4. R4. S5. R5. S6. R6. S7. R7. R7.

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R1. Given
R2. The opposite sides of a parallelogram are parallel (definition).
R3. If 2 R1. Given R2. The opposite sides of a parallelogram are parallel (definition). R3. If 2 lines are cut by a trans, the alternate interior angles are congruent. R4. Same as reason 2 R5. Same as reason 3. R6. Identity R7. ASA lines are cut by a trans, the alternate interior angles are congruent.
R4. Same as reason 2
R5. Same as reason 3.
R6. Identity
R7. ASA

-Suppose that you have already proved that The diagonals of an isosceles trapezoid are congruent. Use this theorem to prove that A pair of base angles of an isosceles trapezoid are congruent. Supply missing statements and missing reasons for the proof. Given: Trapezoid ABCD; and Prove: S1. R1. S2. Draw and R2. S3. R3. S4. R4. Identity S5. R5. S6. R6. -Suppose that you have already proved that "The diagonals of an isosceles trapezoid are congruent." Use this theorem to prove that "A pair of base angles of an isosceles trapezoid are congruent." Supply missing statements and missing reasons for the proof. Given: Trapezoid ABCD; -Suppose that you have already proved that The diagonals of an isosceles trapezoid are congruent. Use this theorem to prove that A pair of base angles of an isosceles trapezoid are congruent. Supply missing statements and missing reasons for the proof. Given: Trapezoid ABCD; and Prove: S1. R1. S2. Draw and R2. S3. R3. S4. R4. Identity S5. R5. S6. R6. and -Suppose that you have already proved that The diagonals of an isosceles trapezoid are congruent. Use this theorem to prove that A pair of base angles of an isosceles trapezoid are congruent. Supply missing statements and missing reasons for the proof. Given: Trapezoid ABCD; and Prove: S1. R1. S2. Draw and R2. S3. R3. S4. R4. Identity S5. R5. S6. R6. Prove: -Suppose that you have already proved that The diagonals of an isosceles trapezoid are congruent. Use this theorem to prove that A pair of base angles of an isosceles trapezoid are congruent. Supply missing statements and missing reasons for the proof. Given: Trapezoid ABCD; and Prove: S1. R1. S2. Draw and R2. S3. R3. S4. R4. Identity S5. R5. S6. R6. S1. R1. S2. Draw -Suppose that you have already proved that The diagonals of an isosceles trapezoid are congruent. Use this theorem to prove that A pair of base angles of an isosceles trapezoid are congruent. Supply missing statements and missing reasons for the proof. Given: Trapezoid ABCD; and Prove: S1. R1. S2. Draw and R2. S3. R3. S4. R4. Identity S5. R5. S6. R6. and -Suppose that you have already proved that The diagonals of an isosceles trapezoid are congruent. Use this theorem to prove that A pair of base angles of an isosceles trapezoid are congruent. Supply missing statements and missing reasons for the proof. Given: Trapezoid ABCD; and Prove: S1. R1. S2. Draw and R2. S3. R3. S4. R4. Identity S5. R5. S6. R6. R2. S3. -Suppose that you have already proved that The diagonals of an isosceles trapezoid are congruent. Use this theorem to prove that A pair of base angles of an isosceles trapezoid are congruent. Supply missing statements and missing reasons for the proof. Given: Trapezoid ABCD; and Prove: S1. R1. S2. Draw and R2. S3. R3. S4. R4. Identity S5. R5. S6. R6. R3. S4. R4. Identity S5. -Suppose that you have already proved that The diagonals of an isosceles trapezoid are congruent. Use this theorem to prove that A pair of base angles of an isosceles trapezoid are congruent. Supply missing statements and missing reasons for the proof. Given: Trapezoid ABCD; and Prove: S1. R1. S2. Draw and R2. S3. R3. S4. R4. Identity S5. R5. S6. R6. R5. S6. -Suppose that you have already proved that The diagonals of an isosceles trapezoid are congruent. Use this theorem to prove that A pair of base angles of an isosceles trapezoid are congruent. Supply missing statements and missing reasons for the proof. Given: Trapezoid ABCD; and Prove: S1. R1. S2. Draw and R2. S3. R3. S4. R4. Identity S5. R5. S6. R6. R6.

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Question 3
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S1. Trapezoid ABCD; S1. Trapezoid ABCD; and R1. Given R2. Through 2 points, there is exactly one line. R3. The diagonals of an isosceles trapezoid are congruent. S4. R5. SSS R6. CPCTC and S1. Trapezoid ABCD; and R1. Given R2. Through 2 points, there is exactly one line. R3. The diagonals of an isosceles trapezoid are congruent. S4. R5. SSS R6. CPCTC R1. Given
R2. Through 2 points, there is exactly one line.
R3. The diagonals of an isosceles trapezoid are congruent.
S4. S1. Trapezoid ABCD; and R1. Given R2. Through 2 points, there is exactly one line. R3. The diagonals of an isosceles trapezoid are congruent. S4. R5. SSS R6. CPCTC R5. SSS
R6. CPCTC

-Provide missing statements and missing reasons for the following proof. Given: ; diagonals and intersect at point P Prove: and S1. R1. Given S2. R2. S3. and R3. S4. R4. S5. R5. ASA S6. R6. -Provide missing statements and missing reasons for the following proof. Given: -Provide missing statements and missing reasons for the following proof. Given: ; diagonals and intersect at point P Prove: and S1. R1. Given S2. R2. S3. and R3. S4. R4. S5. R5. ASA S6. R6. ; diagonals -Provide missing statements and missing reasons for the following proof. Given: ; diagonals and intersect at point P Prove: and S1. R1. Given S2. R2. S3. and R3. S4. R4. S5. R5. ASA S6. R6. and -Provide missing statements and missing reasons for the following proof. Given: ; diagonals and intersect at point P Prove: and S1. R1. Given S2. R2. S3. and R3. S4. R4. S5. R5. ASA S6. R6. intersect at point P Prove: -Provide missing statements and missing reasons for the following proof. Given: ; diagonals and intersect at point P Prove: and S1. R1. Given S2. R2. S3. and R3. S4. R4. S5. R5. ASA S6. R6. and -Provide missing statements and missing reasons for the following proof. Given: ; diagonals and intersect at point P Prove: and S1. R1. Given S2. R2. S3. and R3. S4. R4. S5. R5. ASA S6. R6. S1. R1. Given S2. -Provide missing statements and missing reasons for the following proof. Given: ; diagonals and intersect at point P Prove: and S1. R1. Given S2. R2. S3. and R3. S4. R4. S5. R5. ASA S6. R6. R2. S3. -Provide missing statements and missing reasons for the following proof. Given: ; diagonals and intersect at point P Prove: and S1. R1. Given S2. R2. S3. and R3. S4. R4. S5. R5. ASA S6. R6. and -Provide missing statements and missing reasons for the following proof. Given: ; diagonals and intersect at point P Prove: and S1. R1. Given S2. R2. S3. and R3. S4. R4. S5. R5. ASA S6. R6. R3. S4. -Provide missing statements and missing reasons for the following proof. Given: ; diagonals and intersect at point P Prove: and S1. R1. Given S2. R2. S3. and R3. S4. R4. S5. R5. ASA S6. R6. R4. S5. R5. ASA S6. R6.

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Question 4

-Given the rhombus RSTV, diagonals and intersect at point W. Explain why it follows that . -Given the rhombus RSTV, diagonals -Given the rhombus RSTV, diagonals and intersect at point W. Explain why it follows that . and -Given the rhombus RSTV, diagonals and intersect at point W. Explain why it follows that . intersect at point W. Explain why it follows that -Given the rhombus RSTV, diagonals and intersect at point W. Explain why it follows that . .

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Question 5

-Provide missing statements and missing reasons for the proof of the following theorem. The diagonals of a rhombus are perpendicular. Given: Rhombus ABCD; diagonals and intersect at point X Prove: S1. R1. S2. R2. The diagonals of a rhombus ( ) bisect each other. S3. R3. S4. R4. All sides of a rhombus are congruent. S5. R5. SSS S6. R6. S7. R7. -Provide missing statements and missing reasons for the proof of the following theorem. "The diagonals of a rhombus are perpendicular." Given: Rhombus ABCD; diagonals -Provide missing statements and missing reasons for the proof of the following theorem. The diagonals of a rhombus are perpendicular. Given: Rhombus ABCD; diagonals and intersect at point X Prove: S1. R1. S2. R2. The diagonals of a rhombus ( ) bisect each other. S3. R3. S4. R4. All sides of a rhombus are congruent. S5. R5. SSS S6. R6. S7. R7. and -Provide missing statements and missing reasons for the proof of the following theorem. The diagonals of a rhombus are perpendicular. Given: Rhombus ABCD; diagonals and intersect at point X Prove: S1. R1. S2. R2. The diagonals of a rhombus ( ) bisect each other. S3. R3. S4. R4. All sides of a rhombus are congruent. S5. R5. SSS S6. R6. S7. R7. intersect at point X Prove: -Provide missing statements and missing reasons for the proof of the following theorem. The diagonals of a rhombus are perpendicular. Given: Rhombus ABCD; diagonals and intersect at point X Prove: S1. R1. S2. R2. The diagonals of a rhombus ( ) bisect each other. S3. R3. S4. R4. All sides of a rhombus are congruent. S5. R5. SSS S6. R6. S7. R7. S1. R1. S2. -Provide missing statements and missing reasons for the proof of the following theorem. The diagonals of a rhombus are perpendicular. Given: Rhombus ABCD; diagonals and intersect at point X Prove: S1. R1. S2. R2. The diagonals of a rhombus ( ) bisect each other. S3. R3. S4. R4. All sides of a rhombus are congruent. S5. R5. SSS S6. R6. S7. R7. R2. The diagonals of a rhombus ( -Provide missing statements and missing reasons for the proof of the following theorem. The diagonals of a rhombus are perpendicular. Given: Rhombus ABCD; diagonals and intersect at point X Prove: S1. R1. S2. R2. The diagonals of a rhombus ( ) bisect each other. S3. R3. S4. R4. All sides of a rhombus are congruent. S5. R5. SSS S6. R6. S7. R7. ) bisect each other. S3. -Provide missing statements and missing reasons for the proof of the following theorem. The diagonals of a rhombus are perpendicular. Given: Rhombus ABCD; diagonals and intersect at point X Prove: S1. R1. S2. R2. The diagonals of a rhombus ( ) bisect each other. S3. R3. S4. R4. All sides of a rhombus are congruent. S5. R5. SSS S6. R6. S7. R7. R3. S4. R4. All sides of a rhombus are congruent. S5. R5. SSS S6. -Provide missing statements and missing reasons for the proof of the following theorem. The diagonals of a rhombus are perpendicular. Given: Rhombus ABCD; diagonals and intersect at point X Prove: S1. R1. S2. R2. The diagonals of a rhombus ( ) bisect each other. S3. R3. S4. R4. All sides of a rhombus are congruent. S5. R5. SSS S6. R6. S7. R7. R6. S7. R7.

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Question 6

-Provide missing statements and missing reasons for the proof of this theorem. In a kite, one pair of opposite angles are congruent. Given: Kite ABCD with and Prove: S1. R1. S2. Draw R2. S3. R3. S4. R4. SSS S5. R5. -Provide missing statements and missing reasons for the proof of this theorem. "In a kite, one pair of opposite angles are congruent." Given: Kite ABCD with -Provide missing statements and missing reasons for the proof of this theorem. In a kite, one pair of opposite angles are congruent. Given: Kite ABCD with and Prove: S1. R1. S2. Draw R2. S3. R3. S4. R4. SSS S5. R5. and -Provide missing statements and missing reasons for the proof of this theorem. In a kite, one pair of opposite angles are congruent. Given: Kite ABCD with and Prove: S1. R1. S2. Draw R2. S3. R3. S4. R4. SSS S5. R5. Prove: -Provide missing statements and missing reasons for the proof of this theorem. In a kite, one pair of opposite angles are congruent. Given: Kite ABCD with and Prove: S1. R1. S2. Draw R2. S3. R3. S4. R4. SSS S5. R5. S1. R1. S2. Draw -Provide missing statements and missing reasons for the proof of this theorem. In a kite, one pair of opposite angles are congruent. Given: Kite ABCD with and Prove: S1. R1. S2. Draw R2. S3. R3. S4. R4. SSS S5. R5. R2. S3. -Provide missing statements and missing reasons for the proof of this theorem. In a kite, one pair of opposite angles are congruent. Given: Kite ABCD with and Prove: S1. R1. S2. Draw R2. S3. R3. S4. R4. SSS S5. R5. R3. S4. R4. SSS S5. R5.

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Question 7

-Provide all statements and all reasons for the following proof. Given: , , , and Prove: Quad. ABCD is a parallelogram -Provide all statements and all reasons for the following proof. Given: -Provide all statements and all reasons for the following proof. Given: , , , and Prove: Quad. ABCD is a parallelogram , -Provide all statements and all reasons for the following proof. Given: , , , and Prove: Quad. ABCD is a parallelogram , -Provide all statements and all reasons for the following proof. Given: , , , and Prove: Quad. ABCD is a parallelogram , and -Provide all statements and all reasons for the following proof. Given: , , , and Prove: Quad. ABCD is a parallelogram Prove: Quad. ABCD is a parallelogram

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Question 8

-Use the drawing shown to explain the following theorem. The length of the median of a trapezoid equals one-half the sum of the lengths of the two bases. Given: Trapezoid ABCD with median Prove: [Hint: X is the midpoint of auxiliary diagonal .] -Use the drawing shown to explain the following theorem. "The length of the median of a trapezoid equals one-half the sum of the lengths of the two bases." Given: Trapezoid ABCD with median -Use the drawing shown to explain the following theorem. The length of the median of a trapezoid equals one-half the sum of the lengths of the two bases. Given: Trapezoid ABCD with median Prove: [Hint: X is the midpoint of auxiliary diagonal .] Prove: -Use the drawing shown to explain the following theorem. The length of the median of a trapezoid equals one-half the sum of the lengths of the two bases. Given: Trapezoid ABCD with median Prove: [Hint: X is the midpoint of auxiliary diagonal .] [Hint: X is the midpoint of auxiliary diagonal -Use the drawing shown to explain the following theorem. The length of the median of a trapezoid equals one-half the sum of the lengths of the two bases. Given: Trapezoid ABCD with median Prove: [Hint: X is the midpoint of auxiliary diagonal .] .]

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Question 9

-Consider the drawing provided. Using the auxiliary diagonals (shown dashed), explain why the opposite angles and opposite sides of a parallelogram must be congruent. -Consider the drawing provided. Using the auxiliary diagonals (shown dashed), explain why the "opposite angles and opposite sides of a parallelogram must be congruent."

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Question 10

-Supply all statements and all reasons for the following proof. Given: ; M is the midpoint of and N is the midpoint of Prove: MNAB is a trapezoid -Supply all statements and all reasons for the following proof. Given: -Supply all statements and all reasons for the following proof. Given: ; M is the midpoint of and N is the midpoint of Prove: MNAB is a trapezoid ; M is the midpoint of -Supply all statements and all reasons for the following proof. Given: ; M is the midpoint of and N is the midpoint of Prove: MNAB is a trapezoid and N is the midpoint of -Supply all statements and all reasons for the following proof. Given: ; M is the midpoint of and N is the midpoint of Prove: MNAB is a trapezoid Prove: MNAB is a trapezoid

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Question 11

-Supply missing statements and missing reasons for the following proof. Given: Rectangle MNPQ with diagonals and Prove: S1. R1. S2. and are rt. R2. S3. R3. S4. R4. The diagonals of a rectangle are congruent. S5. R5. -Supply missing statements and missing reasons for the following proof. Given: Rectangle MNPQ with diagonals -Supply missing statements and missing reasons for the following proof. Given: Rectangle MNPQ with diagonals and Prove: S1. R1. S2. and are rt. R2. S3. R3. S4. R4. The diagonals of a rectangle are congruent. S5. R5. and -Supply missing statements and missing reasons for the following proof. Given: Rectangle MNPQ with diagonals and Prove: S1. R1. S2. and are rt. R2. S3. R3. S4. R4. The diagonals of a rectangle are congruent. S5. R5. Prove: -Supply missing statements and missing reasons for the following proof. Given: Rectangle MNPQ with diagonals and Prove: S1. R1. S2. and are rt. R2. S3. R3. S4. R4. The diagonals of a rectangle are congruent. S5. R5. S1. R1. S2. -Supply missing statements and missing reasons for the following proof. Given: Rectangle MNPQ with diagonals and Prove: S1. R1. S2. and are rt. R2. S3. R3. S4. R4. The diagonals of a rectangle are congruent. S5. R5. and -Supply missing statements and missing reasons for the following proof. Given: Rectangle MNPQ with diagonals and Prove: S1. R1. S2. and are rt. R2. S3. R3. S4. R4. The diagonals of a rectangle are congruent. S5. R5. are rt. -Supply missing statements and missing reasons for the following proof. Given: Rectangle MNPQ with diagonals and Prove: S1. R1. S2. and are rt. R2. S3. R3. S4. R4. The diagonals of a rectangle are congruent. S5. R5. R2. S3. -Supply missing statements and missing reasons for the following proof. Given: Rectangle MNPQ with diagonals and Prove: S1. R1. S2. and are rt. R2. S3. R3. S4. R4. The diagonals of a rectangle are congruent. S5. R5. R3. S4. R4. The diagonals of a rectangle are congruent. S5. R5.

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Question 12

-Provide the missing statements abd nissing reasons for the proof of this theorem. If both pairs of opposite sides of a quadrilateral are congruent, the quadrilateral is a parallelogram. Given: Quad. MNPQ; and Prove: MNPQ is a parallelogram S1. R1. Given S2. Draw diagonal R2. S3. R3. Identity S4. R4. SSS S5. R5. S6. R6. If 2 lines are cut by a trans. so that alternate interior angles are congruent, these lines are parallel. S7. R7. S8. R8. S9. R9. -Provide the missing statements abd nissing reasons for the proof of this theorem. "If both pairs of opposite sides of a quadrilateral are congruent, the quadrilateral is a parallelogram." Given: Quad. MNPQ; -Provide the missing statements abd nissing reasons for the proof of this theorem. If both pairs of opposite sides of a quadrilateral are congruent, the quadrilateral is a parallelogram. Given: Quad. MNPQ; and Prove: MNPQ is a parallelogram S1. R1. Given S2. Draw diagonal R2. S3. R3. Identity S4. R4. SSS S5. R5. S6. R6. If 2 lines are cut by a trans. so that alternate interior angles are congruent, these lines are parallel. S7. R7. S8. R8. S9. R9. and -Provide the missing statements abd nissing reasons for the proof of this theorem. If both pairs of opposite sides of a quadrilateral are congruent, the quadrilateral is a parallelogram. Given: Quad. MNPQ; and Prove: MNPQ is a parallelogram S1. R1. Given S2. Draw diagonal R2. S3. R3. Identity S4. R4. SSS S5. R5. S6. R6. If 2 lines are cut by a trans. so that alternate interior angles are congruent, these lines are parallel. S7. R7. S8. R8. S9. R9. Prove: MNPQ is a parallelogram S1. R1. Given S2. Draw diagonal -Provide the missing statements abd nissing reasons for the proof of this theorem. If both pairs of opposite sides of a quadrilateral are congruent, the quadrilateral is a parallelogram. Given: Quad. MNPQ; and Prove: MNPQ is a parallelogram S1. R1. Given S2. Draw diagonal R2. S3. R3. Identity S4. R4. SSS S5. R5. S6. R6. If 2 lines are cut by a trans. so that alternate interior angles are congruent, these lines are parallel. S7. R7. S8. R8. S9. R9. R2. S3. R3. Identity S4. R4. SSS S5. -Provide the missing statements abd nissing reasons for the proof of this theorem. If both pairs of opposite sides of a quadrilateral are congruent, the quadrilateral is a parallelogram. Given: Quad. MNPQ; and Prove: MNPQ is a parallelogram S1. R1. Given S2. Draw diagonal R2. S3. R3. Identity S4. R4. SSS S5. R5. S6. R6. If 2 lines are cut by a trans. so that alternate interior angles are congruent, these lines are parallel. S7. R7. S8. R8. S9. R9. R5. S6. R6. If 2 lines are cut by a trans. so that alternate interior angles are congruent, these lines are parallel. S7. -Provide the missing statements abd nissing reasons for the proof of this theorem. If both pairs of opposite sides of a quadrilateral are congruent, the quadrilateral is a parallelogram. Given: Quad. MNPQ; and Prove: MNPQ is a parallelogram S1. R1. Given S2. Draw diagonal R2. S3. R3. Identity S4. R4. SSS S5. R5. S6. R6. If 2 lines are cut by a trans. so that alternate interior angles are congruent, these lines are parallel. S7. R7. S8. R8. S9. R9. R7. S8. -Provide the missing statements abd nissing reasons for the proof of this theorem. If both pairs of opposite sides of a quadrilateral are congruent, the quadrilateral is a parallelogram. Given: Quad. MNPQ; and Prove: MNPQ is a parallelogram S1. R1. Given S2. Draw diagonal R2. S3. R3. Identity S4. R4. SSS S5. R5. S6. R6. If 2 lines are cut by a trans. so that alternate interior angles are congruent, these lines are parallel. S7. R7. S8. R8. S9. R9. R8. S9. R9.

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Question 13

-Supply missing statements and missing reasons for this proof. Given: Kite MNPQ with diagonal ; and Prove: bisects S1. R1. S2. R2. In a kite, one pair of opposite angles are congruent. S3. R3. S4. R4. S5. R5. -Supply missing statements and missing reasons for this proof. Given: Kite MNPQ with diagonal -Supply missing statements and missing reasons for this proof. Given: Kite MNPQ with diagonal ; and Prove: bisects S1. R1. S2. R2. In a kite, one pair of opposite angles are congruent. S3. R3. S4. R4. S5. R5. ; -Supply missing statements and missing reasons for this proof. Given: Kite MNPQ with diagonal ; and Prove: bisects S1. R1. S2. R2. In a kite, one pair of opposite angles are congruent. S3. R3. S4. R4. S5. R5. and -Supply missing statements and missing reasons for this proof. Given: Kite MNPQ with diagonal ; and Prove: bisects S1. R1. S2. R2. In a kite, one pair of opposite angles are congruent. S3. R3. S4. R4. S5. R5. Prove: -Supply missing statements and missing reasons for this proof. Given: Kite MNPQ with diagonal ; and Prove: bisects S1. R1. S2. R2. In a kite, one pair of opposite angles are congruent. S3. R3. S4. R4. S5. R5. bisects -Supply missing statements and missing reasons for this proof. Given: Kite MNPQ with diagonal ; and Prove: bisects S1. R1. S2. R2. In a kite, one pair of opposite angles are congruent. S3. R3. S4. R4. S5. R5. S1. R1. S2. -Supply missing statements and missing reasons for this proof. Given: Kite MNPQ with diagonal ; and Prove: bisects S1. R1. S2. R2. In a kite, one pair of opposite angles are congruent. S3. R3. S4. R4. S5. R5. R2. In a kite, one pair of opposite angles are congruent. S3. -Supply missing statements and missing reasons for this proof. Given: Kite MNPQ with diagonal ; and Prove: bisects S1. R1. S2. R2. In a kite, one pair of opposite angles are congruent. S3. R3. S4. R4. S5. R5. R3. S4. -Supply missing statements and missing reasons for this proof. Given: Kite MNPQ with diagonal ; and Prove: bisects S1. R1. S2. R2. In a kite, one pair of opposite angles are congruent. S3. R3. S4. R4. S5. R5. R4. S5. R5.

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Question 14
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