Question 1

&#10;Supply missing statements and missing reasons for the following proof.&#10;Given: Chords   and   intersect at point N in   Prove:     )&#10;S1. R1.&#10;S2. Draw   R2.&#10;S3.   R3. The measure of an ext.   of a   is   the sum&#10;of measures of the two nonadjacent int.   . S4.   and   R4.&#10;S5. R5. Substitution Property of Equality&#10;S6. R6. Substitution Property of Equality

Accepted Answer

S1. Chords S1. Chords and intersect at point N in R1. Given R2. Through 2 points, there is exactly one line. R4. In a circle, the measure of an inscribed angle is one-half that of its intercepted arc. S5. S6. )

S1. Chords and intersect at point N in R1. Given R2. Through 2 points, there is exactly one line. R4. In a circle, the measure of an inscribed angle is one-half that of its intercepted arc. S5. S6. )

and

intersect at point N in S1. Chords and intersect at point N in R1. Given R2. Through 2 points, there is exactly one line. R4. In a circle, the measure of an inscribed angle is one-half that of its intercepted arc. S5. S6. )

R1. Given
R2. Through 2 points, there is exactly one line.
R4. In a circle, the measure of an inscribed angle is one-half that of its intercepted arc.
S5. S1. Chords and intersect at point N in R1. Given R2. Through 2 points, there is exactly one line. R4. In a circle, the measure of an inscribed angle is one-half that of its intercepted arc. S5. S6. )

S6.

)

Question 2

&#10;Supply missing statements and missing reasons for the proof of the following theorem.&#10;&#34;An angle inscribed in a semicircle is a right angle.&#34;&#10;Given:   with diameter   and   (as shown)&#10;Prove:   is a right angle.&#10;S1. R1.&#10;S2.   R2.&#10;S3. R3. The measure of a semicircle is 180.&#10;S4.   or   R4.&#10;S5. R5.

Accepted Answer

S1.   with diameter   and   (as shown)&#10;R1. Given&#10;R2. The measure of an inscribed angle is on-half the degree measure of its intercepted arc.&#10;S3.     R4. Substitution Property of Equality&#10;S5.   is a right angle.&#10;R5. Definition of a right angle.

Question 3

&#10;Use the drawing provided to explain why the following theorem is true.&#10;&#34;The tangent segments to a circle from an external point are congruent.&#34;&#10;Given:   and   are tangent to   Prove:   [Hint: Use auxiliary line segment   .]

Accepted Answer

Draw

. Now

and

because the measure of an angle formed by a tangent and chord at the point of contact is one-half the measure of the intercepted arc.
Then Draw . Now and because the measure of an angle formed by a tangent and chord at the point of contact is one-half the measure of the intercepted arc. Then by substitution, so . Then because these sides lie opposite the congruent angles of .

by substitution, so Draw . Now and because the measure of an angle formed by a tangent and chord at the point of contact is one-half the measure of the intercepted arc. Then by substitution, so . Then because these sides lie opposite the congruent angles of .

. Then

because these sides lie opposite the congruent angles of Draw . Now and because the measure of an angle formed by a tangent and chord at the point of contact is one-half the measure of the intercepted arc. Then by substitution, so . Then because these sides lie opposite the congruent angles of .

.

Question 4

&#10;Supply missing statements and missing reasons for the following proof.&#10;Given: Chords   ,   ,   , and   as shown&#10;Prove:   S1. R1.&#10;S2.   R2.&#10;S3. R3. If 2 inscribed   intercept the same arc, these   are   .&#10;S4. R4.

Accepted Answer

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Question 5

&#10;Supply missing statements and missing reasons for the following proof.&#10;Given:     in   Prove:   is an isosceles triangle&#10;S1. R1.&#10;S2.     R2.&#10;S3.     R3.&#10;S4. ? and ? R4. The degree measure of an iscribed angle is equal to one-half&#10;the degree measure of its intercepted arc.&#10;S5.   R5.&#10;S6. R6. Definition of congruent angles&#10;S7. R7. If two angles of a triangle are congruent, then the two sides&#10;that lie opposite those angles are also congruent.&#10;S8. R8.

Accepted Answer

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Question 6

&#10;Supply missing reasons for the following proof.&#10;Given:   with diameter   Prove:   S1.   with diameter   R1.&#10;S2. Draw radius   R2.&#10;S3.   R3.&#10;S4.   R4.&#10;S5.   R5.&#10;S6.   R6.&#10;S7.   or R7.   S8.   R8.&#10;S9. But   R9.&#10;S10. Then   R10.

Accepted Answer

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Question 7

Explain why the following must be true.&#10;Given: Points A, B, and C lie on   in such a way that     ;&#10;also, chords   ,   , and   (no drawing provided)&#10;Prove:   must be an isosceles triangle.

Accepted Answer

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Question 8

&#10;Supply all statements and all reasons for the proof that follows.&#10;Given:   ;   Prove:

Accepted Answer

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Question 9

&#10;Supply missing statements and missing reasons for the following proof.&#10;Given: In the circle,   Prove:     S1. R1.&#10;S2. Draw   R2.&#10;S3.   R3.&#10;S4. R4. Congruent angles have equal measures.&#10;S5. ? and ? R5. The measure of an inscribed angle equals one-half&#10;the measure of its intercepted arc.&#10;S6.     R6.&#10;S7.     R7.&#10;S8. R8.

Accepted Answer

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Question 10

&#10;Supply missing statements and missing reasons for the following proof.&#10;Given:   ; chords   and   intersect at point V&#10;Prove:   S1. R1.&#10;S2. Draw   and   . R2.&#10;S3. R3. Vertical angles are congruent.&#10;S4.   R4.&#10;S5. R5. AA&#10;S6.   R6.&#10;S7. R7. Means-Extremes Property of a Proportion

Accepted Answer

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Deck 6: Circles