Question 1

Solve.
-Explain how to construct a parallelogram given two adjacent sides. If it is not possible, explain why.

Accepted Answer

The answer of Solve.
-Explain how to construct a parallelogram given...

Question 2

Answer the question.
-A quadrilateral is a______ if and only if opposite sides are parallel or congruent.

Accepted Answer

The answer of Answer the question.
-A quadrilateral is a______ if...

Question 3

Provide the requested proof.
-$$\text { In the figure below, } \mathrm { AC } = \mathrm { AD } \text { and } \angle \mathrm { BAC } \cong \angle  \mathrm { DAE } \text {. Prove that the triangle } \mathrm { ABE } \text { is isosceles. }$$

Accepted Answer

The answer of Provide the requested proof.
-\[\text { In the...

Question 4

If a rectangle is a square, it must also be a rhombus.

Accepted Answer

A) True 
 B)False

Question 5

These triangles are similar. Find the missing length.
-

Accepted Answer

A)  3 
B)  4 
C)  5 
D)  6

Question 6

Solve.
-Describe how to draw a square so that a given circle circumscribes the square.

Accepted Answer

The answer of Solve.
-Describe how to draw a square so...

Question 7

Use a ruler, protractor, and compass to construct, if possible, a triangle with the stated properties. If such a triangle cannot be drawn, explain why. Decide if there can be two or more noncongruent triangles with the stated properties.
-A triangle with sides of length 19 cm, 9 cm, and 26 cm

Accepted Answer

A) Exactly one such triangle can be constructed. 
B) No such triangle can be constructed. 
C) Two or more such noncongruent triangles can be constructed.

Question 8

Provide the requested proof.
-Suppose polygon $\mathrm { ABCD }$ is any square with diagonals $\overline { \mathrm { AC } }$ and $\overline { \mathrm { BD } }$ intersecting at point $\mathrm { F }$.

What can be said about any point on $\overline { \mathrm { AF } }$ and points $\mathrm { B }$ and $\mathrm { D }$ ?

Accepted Answer

The answer of Provide the requested proof.
-Suppose polygon \(\mathrm {...

Question 9

These triangles are similar. Find the missing length.
-

Accepted Answer

A)  $x = 13$ 
B)  $x = 9$ 
C)  $x = 18$ 
D)  $x = 27$

Question 10

State whether the triangles are congruent. If the information given is not sufficient, state "No conclusion possible".
-

Accepted Answer

A)  Congruent 
B)  Not congruent 
C)  No conclusion possible

Question 11

Answer the question.
-A tree casts a shadow 40 meters long. At the same time, the shadow cast by a vertical 5 meter stick is 10 meters long. Find the height of the tree.

Accepted Answer

A) 80 
B) 50 
C) 20 
D)  $\frac { 5 } { 4 }$

Question 12

State whether the triangles are congruent. If the information given is not sufficient, state "No conclusion possible".
-

Accepted Answer

A)  Congruent 
B)  Not congruent 
C)  No conclusion possible

Question 13

State whether the triangles are congruent. If the information given is not sufficient, state "No conclusion possible".
-

Accepted Answer

A)  Not congruent 
B)  Congruent 
C)  No conclusion possible

Question 14

Solve.
-Given a right triangle ABC, explain how to construct an altitude from vertex A.

Accepted Answer

The answer of Solve.
-Given a right triangle ABC, explain how...

Question 15

Solve.
-Given $\overline { \mathrm { AB } }$, construct the perpendicular bisector of $\overline { \mathrm { AB } }$ without putting any marks below $\overline { \mathrm { AB } }$.

Accepted Answer

The answer of Solve.
-Given \(\overline { \mathrm { AB }...

Question 16

Solve.
-Explain how to construct a triangle with two obtuse angles. If it is not possible, explain why.

Accepted Answer

The answer of Solve.
-Explain how to construct a triangle with...

Question 17

Answer the question.
-What type of figure is formed by joining the midpoints of the adjacent sides of a rectangle?

Accepted Answer

The answer of Answer the question.
-What type of figure is...

Question 18

A sector of a circle is a pie-shaped section bounded by two radii and an arc. What is a
minimal set of conditions for determining that two sectors of the same circle are congruent?

Accepted Answer

The answer of A sector of a circle is a...

Question 19

Answer the question.
-Are two regular pentagons always similar? Explain why or why not.

Accepted Answer

The answer of Answer the question.
-Are two regular pentagons always...

Question 20

Provide the requested proof.
-$$\text { In the figure below, } \mathrm { AB } = \mathrm { CD } , \mathrm { BE } = \mathrm { FC } \text { and } \angle \mathrm { B } \cong \angle \mathrm { C } \text {. Prove that } \mathrm { AF } = \mathrm { ED } \text {. }$$

Accepted Answer

The answer of Provide the requested proof.
-\[\text { In the...

Exam 12: Congruence and Similarity With Constructions

Solve. -Explain how to construct a parallelogram given two adjacent sides. If it is not possible, explain why.

Answer the question. -A quadrilateral is a______ if and only if opposite sides are parallel or congruent.

If a rectangle is a square, it must also be a rhombus.

These triangles are similar. Find the missing length. -

Solve. -Describe how to draw a square so that a given circle circumscribes the square.

Use a ruler, protractor, and compass to construct, if possible, a triangle with the stated properties. If such a triangle cannot be drawn, explain why. Decide if there can be two or more noncongruent triangles with the stated properties. -A triangle with sides of length 19 cm, 9 cm, and 26 cm

These triangles are similar. Find the missing length. -

State whether the triangles are congruent. If the information given is not sufficient, state "No conclusion possible". -

Answer the question. -A tree casts a shadow 40 meters long. At the same time, the shadow cast by a vertical 5 meter stick is 10 meters long. Find the height of the tree.

State whether the triangles are congruent. If the information given is not sufficient, state "No conclusion possible". -

State whether the triangles are congruent. If the information given is not sufficient, state "No conclusion possible". -

Solve. -Given a right triangle ABC, explain how to construct an altitude from vertex A.

Solve. -Given AB‾\overline { \mathrm { AB } }AB , construct the perpendicular bisector of AB‾\overline { \mathrm { AB } }AB without putting any marks below AB‾\overline { \mathrm { AB } }AB .

Solve. -Explain how to construct a triangle with two obtuse angles. If it is not possible, explain why.

Answer the question. -What type of figure is formed by joining the midpoints of the adjacent sides of a rectangle?

A sector of a circle is a pie-shaped section bounded by two radii and an arc. What is a minimal set of conditions for determining that two sectors of the same circle are congruent?

Answer the question. -Are two regular pentagons always similar? Explain why or why not.