Question 1

Solve.
-Inscribe a circle into a kite.

Accepted Answer

The answer of Solve.
-Inscribe a circle into a kite....

Question 2

Provide the requested proof.
-Let $\mathrm { ABC }$ be an isosceles triangle with $\angle \mathrm { B } \cong \angle C$. Suppose that $M$ is a point on $B C$ such that $\overline { \mathrm { AM } }$ is perpendicular to $\overline { \mathrm { BC } }$. Prove that $\mathrm { M }$ is the midpoint of $\overline { \mathrm { BC } }$.

Accepted Answer

Answers will vary. A sample co

Question 3

Solve.
-Consider the two congruent equilateral 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 two congruent equilateral triangles ABC...

Question 4

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

Accepted Answer

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

Question 5

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

Accepted Answer

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

Question 6

No square is a trapezoid.

Accepted Answer

A) True 
 B)False

Question 7

Solve.
-Given an equilateral triangle ABC, explain how to construct an altitude form vertex A.

Accepted Answer

Construct a perpendi

Question 8

Provide an appropriate response.
-The two triangles shown below are congruent. $\triangle \mathrm { IJK } \cong$_____

Accepted Answer

A)  $\triangle \mathrm { NLM }$ 
B)  $\triangle \mathrm { NML }$ 
C)  $\triangle \mathrm { MNL }$ 
D)  $\triangle \mathrm { LMN }$ 
A)  $\triangle \mathrm { NLM }$ 
B)  $\triangle \mathrm { NML }$ 
C)  $\triangle \mathrm { MNL }$ 
D)  $\triangle \mathrm { LMN }$

Question 9

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.
-An isosceles triangle with sides of length 6 cm and 15 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. 
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 10

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

Accepted Answer

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

Question 11

Provide an appropriate response.
-The two triangles shown below are congruent. The sides corresponding to $\overline { \mathrm { AB } } , \overline { \mathrm { BC } }$, and $\overline { \mathrm { AC } }$ (in order) are____

Accepted Answer

A)  $\overline { \mathrm { LN } } , \overline { \mathrm { MN } }$, and $\overline { \mathrm { ML } }$ 
B)  $\overline { \mathrm { ML } } , \overline { \mathrm { LN } }$, and $\overline { \mathrm { MN } }$ 
C)  $\overline { \mathrm { MN } } , \overline { \mathrm { LN } }$, and $\overline { \mathrm { ML } }$ 
D)  $\overline { \mathrm { ML } } , \overline { \mathrm { MN } }$, and $\overline { \mathrm { LN } }$ 
A)  $\overline { \mathrm { LN } } , \overline { \mathrm { MN } }$, and $\overline { \mathrm { ML } }$ 
B)  $\overline { \mathrm { ML } } , \overline { \mathrm { LN } }$, and $\overline { \mathrm { MN } }$ 
C)  $\overline { \mathrm { MN } } , \overline { \mathrm { LN } }$, and $\overline { \mathrm { ML } }$ 
D)  $\overline { \mathrm { ML } } , \overline { \mathrm { MN } }$, and $\overline { \mathrm { LN } }$

Question 12

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

Accepted Answer

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

Question 13

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

Accepted Answer

A) None of these. 
B) The measures of one angle in each rhombus must be equal. 
C) The lengths of one side and the measure of one corresponding angle of each rhombus must beequal. 
D) The lengths of two adjacent sides in each rhombus must be equal. 
A) None of these. 
B) The measures of one angle in each rhombus must be equal. 
C) The lengths of one side and the measure of one corresponding angle of each rhombus must beequal. 
D) The lengths of two adjacent sides in each rhombus must be equal.

Question 14

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

Accepted Answer

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

Question 15

Answer the question.
-What is a quadrilateral with diagonals that bisect each other?

Accepted Answer

The answer of Answer the question.
-What is a quadrilateral with...

Question 16

Answer the question.
-When is a parallelogram a rhombus?

Accepted Answer

A parallelogram is a

Question 17

Answer the question.
-A trapezoid is a kite.

Accepted Answer

A) True 
 B)False

Question 18

Tell whether the triangles are similar or not similar.
-

Accepted Answer

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

Question 19

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

Accepted Answer

Construct two perpen

Question 20

Solve.
-Inscribe a circle into a square.

Accepted Answer

The answer of Solve.
-Inscribe a circle into a square....

Solve. -Inscribe a circle into a kite.

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

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

No square is a trapezoid.

Solve. -Given an equilateral triangle ABC, explain how to construct an altitude form vertex A.

Provide an appropriate response. -The two triangles shown below are congruent. $\triangle \mathrm { IJK } \cong$ _ $Provide an appropriate response. -The two triangles shown below are congruent. \triangle \mathrm { IJK } \cong _$

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. -An isosceles triangle with sides of length 6 cm and 15 cm

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

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

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

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

Answer the question. -What is a quadrilateral with diagonals that bisect each other?

Answer the question. -When is a parallelogram a rhombus?

Answer the question. -A trapezoid is a kite.

Tell whether the triangles are similar or not similar. -

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

Solve. -Inscribe a circle into a square.

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. -Inscribe a circle into a kite.

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

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

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

No square is a trapezoid.

Solve. -Given an equilateral triangle ABC, explain how to construct an altitude form vertex A.

Provide an appropriate response. -The two triangles shown below are congruent. △IJK≅\triangle \mathrm { IJK } \cong△IJK≅ _____

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. -An isosceles triangle with sides of length 6 cm and 15 cm

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

Provide an appropriate response. -The two triangles shown below are congruent. The sides corresponding to AB‾,BC‾\overline { \mathrm { AB } } , \overline { \mathrm { BC } }AB,BC , and AC‾\overline { \mathrm { AC } }AC (in order) are____

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

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

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

Answer the question. -What is a quadrilateral with diagonals that bisect each other?

Answer the question. -When is a parallelogram a rhombus?

Answer the question. -A trapezoid is a kite.

Tell whether the triangles are similar or not similar. -

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

Solve. -Inscribe a circle into a square.

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

Provide an appropriate response. -The two triangles shown below are congruent. $\triangle \mathrm { IJK } \cong$ _ $Provide an appropriate response. -The two triangles shown below are congruent. \triangle \mathrm { IJK } \cong _$

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