Question 1

Solve.
-Explain how to construct a line parallel to a line l using the sliding-triangle method.

Accepted Answer

Put the ruler down on line l .

Question 2

These triangles are similar. Find the missing length.
-

Accepted Answer

A)  $x = 11$ 
B)  $x = 12$ 
C)  $x = 4$ 
D)  $x = 16$ 
A)  $x = 11$ 
B)  $x = 12$ 
C)  $x = 4$ 
D)  $x = 16$

Question 3

Provide an appropriate response.
-Use the fact that an isosceles triangle is congruent to itself to answer the following: (i) Write a congruence correspondence between an isosceles $\triangle \mathrm { VWX }$ and itself when $\mathrm { VW } = \mathrm { WX }$. (ii) Use your answer in (i) to show that the the base angles in an isosceles triangle are congruent.

Accepted Answer

A)  (i) $\triangle W X V \cong \triangle W V X$
(ii) $\angle W \cong \angle X$ by CPCTC 
B)  (i) $\triangle \mathrm { WVX } \cong \triangle \mathrm { XWV }$
(ii) $\angle V \cong \angle X$ by CPCTC 
C)  (i) $\triangle W V X \cong \triangle X W V$
(ii) $\angle V \cong \angle W$ by CPCTC 
D)  (i) $\triangle W X V \cong \triangle W V X$
(ii) $\angle V \cong \angle X$ by CPCTC 
A)  (i) $\triangle W X V \cong \triangle W V X$
(ii) $\angle W \cong \angle X$ by CPCTC 
B)  (i) $\triangle \mathrm { WVX } \cong \triangle \mathrm { XWV }$
(ii) $\angle V \cong \angle X$ by CPCTC 
C)  (i) $\triangle W V X \cong \triangle X W V$
(ii) $\angle V \cong \angle W$ by CPCTC 
D)  (i) $\triangle W X V \cong \triangle W V X$
(ii) $\angle V \cong \angle X$ by CPCTC

Question 4

Provide the requested proof.
-In the trapezoid below, $\mathrm { m } ( \angle \mathrm { D } ) = \mathrm { m } ( \angle \mathrm { C } )$ and $\mathrm { AD } = \mathrm { BC }$. If $\mathrm { M }$ is the midpoint of $\overline { \mathrm { CD } }$, prove that $\mathrm { m } ( \angle \mathrm { MAB } ) = \mathrm { m } ( \angle \mathrm { MBA } )$.

Accepted Answer

Answers will vary. A sample co

Question 5

The perpendicular bisectors of a triangle are always concurrent.

Accepted Answer

A) True 
 B)False

Question 6

Solve.
-Given two 15-cm sides and two 10-cm sides, how many quadrilaterals can be formed with a 75° angle?

Accepted Answer

Four quadrilaterals

Question 7

Answer the question.
-Can a parallelogram have exactly three right angles? Explain why or why not.

Accepted Answer

No, because opposite angles of

Question 8

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

Accepted Answer

No. The ratio of the adjacent

Question 9

Answer the question.
-A rectangle is a trapezoid.

Accepted Answer

A) True 
 B)False

Question 10

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 5 cm and 12 cm and an angle of 102°

Accepted Answer

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

Question 11

Provide an appropriate response.
-The two triangles shown below are congruent. The vertices corresponding to H, I, and J (in order) are .

Accepted Answer

A)  $\mathrm { L } , \mathrm { K }$, and $\mathrm { M }$ 
B)  $\mathrm { K } , \mathrm { M }$, and $\mathrm { L }$ 
C)  $\mathrm { M } , \mathrm { K }$, and $\mathrm { L }$ 
D)  $\mathrm { K } , \mathrm { L }$, and $\mathrm { M }$ 
A)  $\mathrm { L } , \mathrm { K }$, and $\mathrm { M }$ 
B)  $\mathrm { K } , \mathrm { M }$, and $\mathrm { L }$ 
C)  $\mathrm { M } , \mathrm { K }$, and $\mathrm { L }$ 
D)  $\mathrm { K } , \mathrm { L }$, and $\mathrm { M }$

Question 12

Solve.
-Explain how to construct a parallelogram with exactly three right angles. If it is not possible, explain why.

Accepted Answer

Not possible. Opposite angles

Question 13

Solve.
-Explain how to construct a line through a point P parallel to a line l using the corresponding-angle method.

Accepted Answer

Through @#LAT-DLM&, draw a line that int

Question 14

Tell whether the triangles are similar or not similar.
-

Accepted Answer

A)  Similar 
B)  Not similar 
A)  Similar 
B)  Not similar

Question 15

Provide the requested proof.
-Let $\mathrm { ABC }$ be a triangle, and let $\mathrm { M }$ be the midpoint of side $\overline { \mathrm { BC } }$. If $\overline { \mathrm { AM } }$ is perpendicular to $\overline { \mathrm { BC } }$, prove that $A B C$ is an isosceles triangle.

Accepted Answer

Answers will vary. A sample co

Question 16

Tell whether the triangles are similar or not similar.
-

Accepted Answer

A)  Similar 
B)  Not similar 
A)  Similar 
B)  Not similar

Question 17

Answer the question.
-A nearby playground has a sandbox. Erica stretches string out to show the diagonals of the sandbox. The diagonals are perpendicular and they bisect each other. Is the sandbox a
square?

Accepted Answer

Not necessarily. It

Question 18

Answer the question.
-A quadrilateral is a_____ if and only if its diagonals are perpendicular.

Accepted Answer

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

Question 19

The radius of a circle that circumscribes a quadrilateral is the distance from the center of the circle
to any of the perpendicular bisectors.

Accepted Answer

A) True 
 B)False

Question 20

Solve.
-Explain how to construct a line through a point P parallel to a line l using the rhombus method.

Accepted Answer

Draw any line through @#LAT-DLM& that intersects 1

Solve. -Explain how to construct a line parallel to a line l using the sliding-triangle method.

These triangles are similar. Find the missing length. -

The perpendicular bisectors of a triangle are always concurrent.

Solve. -Given two 15-cm sides and two 10-cm sides, how many quadrilaterals can be formed with a 75° angle?

Answer the question. -Can a parallelogram have exactly three right angles? Explain why or why not.

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

Answer the question. -A rectangle is a trapezoid.

Provide an appropriate response. -The two triangles shown below are congruent. The vertices corresponding to H, I, and J (in order) are .

Solve. -Explain how to construct a parallelogram with exactly three right angles. If it is not possible, explain why.

Solve. -Explain how to construct a line through a point P parallel to a line l using the corresponding-angle method.

Tell whether the triangles are similar or not similar. -

Provide the requested proof. -Let $\mathrm { ABC }$ be a triangle, and let $\mathrm { M }$ be the midpoint of side $\overline { \mathrm { BC } }$ . If $\overline { \mathrm { AM } }$ is perpendicular to $\overline { \mathrm { BC } }$ , prove that $A B C$ is an isosceles triangle.

Tell whether the triangles are similar or not similar. -

Answer the question. -A nearby playground has a sandbox. Erica stretches string out to show the diagonals of the sandbox. The diagonals are perpendicular and they bisect each other. Is the sandbox a square?

Answer the question. -A quadrilateral is a_____ if and only if its diagonals are perpendicular.

The radius of a circle that circumscribes a quadrilateral is the distance from the center of the circle to any of the perpendicular bisectors.

Solve. -Explain how to construct a line through a point P parallel to a line l using the rhombus method.

An Introduction to Problem Solving

Introduction to Logic and Sets

Numeration Systems and Whole Number Operations

Number Theory

Integers

Rational Numbers and Proportional Reasoning

Rational Numbers As Decimals and Percents

Real Numbers and Algebraic Thinking

Probability

Data Analysisstatistics: an Introduction

Introductory Geometry

Congruence and Similarity With Transformations

Area, Pythagorean Theorem, and Volume

Filters

Exam 12: Congruence and Similarity With Constructions

Solve. -Explain how to construct a line parallel to a line l using the sliding-triangle method.

These triangles are similar. Find the missing length. -

The perpendicular bisectors of a triangle are always concurrent.

Solve. -Given two 15-cm sides and two 10-cm sides, how many quadrilaterals can be formed with a 75° angle?

Answer the question. -Can a parallelogram have exactly three right angles? Explain why or why not.

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

Answer the question. -A rectangle is a trapezoid.

Provide an appropriate response. -The two triangles shown below are congruent. The vertices corresponding to H, I, and J (in order) are .

Solve. -Explain how to construct a parallelogram with exactly three right angles. If it is not possible, explain why.

Solve. -Explain how to construct a line through a point P parallel to a line l using the corresponding-angle method.

Tell whether the triangles are similar or not similar. -

Tell whether the triangles are similar or not similar. -

Answer the question. -A nearby playground has a sandbox. Erica stretches string out to show the diagonals of the sandbox. The diagonals are perpendicular and they bisect each other. Is the sandbox a square?

Answer the question. -A quadrilateral is a_____ if and only if its diagonals are perpendicular.

The radius of a circle that circumscribes a quadrilateral is the distance from the center of the circle to any of the perpendicular bisectors.

Solve. -Explain how to construct a line through a point P parallel to a line l using the rhombus method.

An Introduction to Problem Solving

Introduction to Logic and Sets

Numeration Systems and Whole Number Operations

Number Theory

Integers

Rational Numbers and Proportional Reasoning

Rational Numbers As Decimals and Percents

Real Numbers and Algebraic Thinking

Probability

Data Analysisstatistics: an Introduction

Introductory Geometry

Congruence and Similarity With Transformations

Area, Pythagorean Theorem, and Volume

Filters