Question 1

Solve.
-Given the following triangle, construct the point P that is equidistant from the 3 vertices of the triangle.

Accepted Answer

The answer of Solve.
-Given the following triangle, construct the point...

Question 2

Solve.
-How many different rotational symmetries does a square have?

Accepted Answer

A) 5 
B) 3 
C) 4 
D) 2 
A) 5 
B) 3 
C) 4 
D) 2 B

Question 3

Answer the question.
-A building is 25 feet tall. Its shadow is 50 feet long. A nearby building is 15 feet tall. Find the length of the shadow of the second building.

Accepted Answer

A)  30 
B)  $\frac { 250 } { 3 }$ 
C)  $\frac { 15 } { 2 }$ 
D)  750 
A)  30 
B)  $\frac { 250 } { 3 }$ 
C)  $\frac { 15 } { 2 }$ 
D)  750 A

Question 4

Provide an appropriate response.
-$$\text { Determine whether the given conditions are sufficient to prove that } \triangle D E F \cong \triangle P Q R \text {. Justify your }$$ answer. 
$\overline { \mathrm { DE } } \cong \overline { \mathrm { PQ } } , \overline { \mathrm { EF } } \cong \overline { \mathrm { QR } } , \overline { \mathrm { DF } } \cong \overline { \mathrm { PR } }$

Accepted Answer

A)  Yes; CPCTC 
B)  Yes; SSS 
C)  Conditions are insufficient. 
D)  Yes; SAS 
A)  Yes; CPCTC 
B)  Yes; SSS 
C)  Conditions are insufficient. 
D)  Yes; SAS

Question 5

Solve.
-Construct the perpendicular bisectors of the right triangle.

Accepted Answer

The answer of Solve.
-Construct the perpendicular bisectors of the right...

Question 6

Provide an appropriate response.
-$$\text { Determine whether the given conditions are sufficient to prove that } \triangle \mathrm { MNO } \simeq \triangle \mathrm { STU } \text {. Justify your }$$ answer. $$\overline { \mathrm { MN } } \cong \overline { \mathrm { ST } } , \overline { \mathrm { NO } } \cong \overline { \mathrm { TU } } , \angle \mathrm { N } \cong \angle \mathrm { T }$$

Accepted Answer

A)  Conditions are insufficient. 
B)  Yes; SAS 
C)  Yes; CPCTC 
D)  Yes; SSS 
A)  Conditions are insufficient. 
B)  Yes; SAS 
C)  Yes; CPCTC 
D)  Yes; SSS

Question 7

Provide an appropriate response.
-The two triangles shown below are congruent. The angles corresponding to $\angle , \angle K$, and $\angle$ (in order) are____

Accepted Answer

A)  $\angle S , \angle Q$, and $\angle R$ 
B)  $S S , \angle R$, and $\angle Q$ 
C)  $\angle Q , \angle R$, and $\angle S$ 
D)  $\angle R , \triangle S$, and $\angle Q$ 
A)  $\angle S , \angle Q$, and $\angle R$ 
B)  $S S , \angle R$, and $\angle Q$ 
C)  $\angle Q , \angle R$, and $\angle S$ 
D)  $\angle R , \triangle S$, and $\angle Q$

Question 8

These triangles are similar. Find the missing length.
-

Accepted Answer

A)  x= 28 
B)  $x = 36$ 
C)  $x = 34$ 
D)  $x = 45$ 
A)  x= 28 
B)  $x = 36$ 
C)  $x = 34$ 
D)  $x = 45$

Question 9

Provide an appropriate response.
-For what kind of triangles will the perpendicular bisectors of the sides intersect on a side of the triangle?

Accepted Answer

A) right 
B) none 
C) obtuse 
D) acute 
A) right 
B) none 
C) obtuse 
D) acute

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 11 cm and 11 cm and a nonincluded angle of 46°

Accepted Answer

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

Question 11

Provide the requested proof.
-$$\text { In the trapezoid below, } \mathrm { m } ( \angle \mathrm { D } ) = \mathrm { m } ( \angle \mathrm { C } ) \text {. Prove that } \mathrm { AD } = \mathrm { BC } \text {. }$$

Accepted Answer

Answers will vary. A sample correct resp

Question 12

Solve.
-Describe how to construct a regular octagon in a given circle so that the circle circumscribes the octagon.

Accepted Answer

Draw a diameter of the circle. Construct

Question 13

Answer the question.
-What minimum information is sufficient to determine the congruency of two equilateral triangles?

Accepted Answer

A) The lengths of one side of each triangle must be equal. 
B) The measures of one angle of each triangle must be equal. 
C) None of these. 
D) The lengths of two sides and the included angles of each triangle must be equal. 
A) The lengths of one side of each triangle must be equal. 
B) The measures of one angle of each triangle must be equal. 
C) None of these. 
D) The lengths of two sides and the included angles of each triangle must be equal.

Question 14

Provide an appropriate response.
-$$\text { Determine whether the given conditions are sufficient to prove that } \triangle \mathrm { GHI } \cong \triangle \mathrm { STU } \text {. Justify your }$$ answer. $$\angle \mathrm { U } \cong \angle \mathrm { \textrm {SU } } \cong \overline { \mathrm { GI } } , \overline { \mathrm { ST } } \cong \overline { \mathrm { GH } }$$

Accepted Answer

A)  Yes; CPCTC 
B)  Yes; SSS 
C)  Yes; SAS 
D)  Conditions are insufficient. 
A)  Yes; CPCTC 
B)  Yes; SSS 
C)  Yes; SAS 
D)  Conditions are insufficient.

Question 15

Tell whether the triangles are similar or not similar.
-

Accepted Answer

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

Question 16

Answer the question.
-Is a kite a parallelogram?

Accepted Answer

The answer of Answer the question.
-Is a kite a parallelogram?...

Question 17

Solve.
-Given the following triangle, construct the point P that is equidistant from the 3 vertices of the triangle.

Accepted Answer

The answer of Solve.
-Given the following triangle, construct the point...

Question 18

Solve.
-Explain how to construct a square given one side $\overline { \mathrm { AB } }$ and constructing only parallel lines. If it is not possible, explain why.

Accepted Answer

It isn't possible us

Question 19

Solve.
-Consider the isosceles triangles ABC and PQR. If side AB is glued to side PQ, what type of quadrilateral is formed?

Accepted Answer

The answer of Solve.
-Consider the isosceles triangles ABC and PQR....

Question 20

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 angles measuring 11° and 113° and a nonincluded side of length 11 cm

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.

Solve. -Given the following triangle, construct the point P that is equidistant from the 3 vertices of the triangle.

Solve. -How many different rotational symmetries does a square have?

Answer the question. -A building is 25 feet tall. Its shadow is 50 feet long. A nearby building is 15 feet tall. Find the length of the shadow of the second building.

Solve. -Construct the perpendicular bisectors of the right triangle.

These triangles are similar. Find the missing length. -

Provide an appropriate response. -For what kind of triangles will the perpendicular bisectors of the sides intersect on a side of the triangle?

Solve. -Describe how to construct a regular octagon in a given circle so that the circle circumscribes the octagon.

Answer the question. -What minimum information is sufficient to determine the congruency of two equilateral triangles?

Tell whether the triangles are similar or not similar. -

Answer the question. -Is a kite a parallelogram?

Solve. -Given the following triangle, construct the point P that is equidistant from the 3 vertices of the triangle.

Solve. -Explain how to construct a square given one side $\overline { \mathrm { AB } }$ and constructing only parallel lines. If it is not possible, explain why.

Solve. -Consider the isosceles triangles ABC and PQR. If side AB is glued to side PQ, what type of quadrilateral is formed?

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. -Given the following triangle, construct the point P that is equidistant from the 3 vertices of the triangle.

Solve. -How many different rotational symmetries does a square have?

Answer the question. -A building is 25 feet tall. Its shadow is 50 feet long. A nearby building is 15 feet tall. Find the length of the shadow of the second building.

Solve. -Construct the perpendicular bisectors of the right triangle.

Provide an appropriate response. -The two triangles shown below are congruent. The angles corresponding to ∠,∠K\angle , \angle K∠,∠K , and ∠\angle∠ (in order) are____

These triangles are similar. Find the missing length. -

Provide an appropriate response. -For what kind of triangles will the perpendicular bisectors of the sides intersect on a side of the triangle?

Solve. -Describe how to construct a regular octagon in a given circle so that the circle circumscribes the octagon.

Answer the question. -What minimum information is sufficient to determine the congruency of two equilateral triangles?

Tell whether the triangles are similar or not similar. -

Answer the question. -Is a kite a parallelogram?

Solve. -Given the following triangle, construct the point P that is equidistant from the 3 vertices of the triangle.

Solve. -Explain how to construct a square given one side AB‾\overline { \mathrm { AB } }AB and constructing only parallel lines. If it is not possible, explain why.

Solve. -Consider the isosceles triangles ABC and PQR. If side AB is glued to side PQ, what type of quadrilateral is formed?

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

Solve. -Explain how to construct a square given one side $\overline { \mathrm { AB } }$ and constructing only parallel lines. If it is not possible, explain why.