Question 1

Based on the figure, specify the given set in a simpler way.
-

Accepted Answer

A)  $\overleftrightarrow { \mathrm { AC } }$ 
B)    
C)    
D)  $C$ 
A)  $\overleftrightarrow { \mathrm { AC } }$ 
B)    
C)    
D)  $C$

Question 2

Refer to the given figure, an isosceles triangle with AB = AC.  
-If the perimeter of $\triangle \mathrm { ABC } = 58 \mathrm {~m}$, and $\mathrm { AB } = 25 \mathrm {~m}$, what is the length $\mathrm { BC }$ ?

Accepted Answer

A)  $50 \mathrm {~m}$ 
B)  $56 \mathrm {~m}$ 
C)  $8 \mathrm {~m}$ 
D)  $25 \mathrm {~m}$ 
A)  $50 \mathrm {~m}$ 
B)  $56 \mathrm {~m}$ 
C)  $8 \mathrm {~m}$ 
D)  $25 \mathrm {~m}$

Question 3

Based on the figure, specify the given set in a simpler way.
-

Accepted Answer

A)    
B)  $\varnothing$ 
C)   
D)    
A)    
B)  $\varnothing$ 
C)   
D)

Question 4

Use the properties of parallel lines to solve the problem.
-Assume that m and n are parallel. Find the measures of angles A and B.  
$\angle A=(4 x-5)^{\circ}, \angle B=(3 x+26)^{\circ}$

Accepted Answer

A)  $103 ^ { \circ } , 103 ^ { \circ }$ 
B)  $103 ^ { \circ } , 83 ^ { \circ }$ 
C)  $119 ^ { \circ } , 119 ^ { \circ }$ 
D)  $67 ^ { \circ } , 119 ^ { \circ }$ 
A)  $103 ^ { \circ } , 103 ^ { \circ }$ 
B)  $103 ^ { \circ } , 83 ^ { \circ }$ 
C)  $119 ^ { \circ } , 119 ^ { \circ }$ 
D)  $67 ^ { \circ } , 119 ^ { \circ }$

Question 5

Based on the figure, specify the given set in a simpler way.
-

Accepted Answer

A)  $\overleftrightarrow { \mathrm { AD } }$ 
B)    
C)   
D)   
A)  $\overleftrightarrow { \mathrm { AD } }$ 
B)    
C)   
D)

Question 6

a and b represent the two legs of a right triangle, while c represents the hypotenuse. Find the length of the unknown side.
-$a = 10 \text { in., } b = 24 \text { in. }$

Accepted Answer

A)  $c = 18$ in. 
B)  $c = 25 \mathrm { in } .$ 
C)  $\mathrm { c } = 26 \mathrm { in }$. 
D)  $c = 22 \mathrm { in }$. 
A)  $c = 18$ in. 
B)  $c = 25 \mathrm { in } .$ 
C)  $\mathrm { c } = 26 \mathrm { in }$. 
D)  $c = 22 \mathrm { in }$.

Question 7

Refer to the given figure, an isosceles triangle with AB = AC.  
-If $\angle A$ measures $117 ^ { \circ }$ find the measure of $\angle B$.

Accepted Answer

A)  $31.5 ^ { \circ }$ 
B)  $63 ^ { \circ }$ 
C)  $26.5 ^ { \circ }$ 
D)  $121.5 ^ { \circ }$ 
A)  $31.5 ^ { \circ }$ 
B)  $63 ^ { \circ }$ 
C)  $26.5 ^ { \circ }$ 
D)  $121.5 ^ { \circ }$

Question 8

$\text { Refer to this figure to answer the question. Assume } \overleftrightarrow { \mathrm { CF } } \text { and } \overleftrightarrow { \mathrm { GJ } } \text { are parallel. }$

-Are $\angle D E B$ and $\angle B E F$ adjacent angles?

Accepted Answer

A)  No 
B)  Yes 
A)  No 
B)  Yes

Question 9

Solve the problem.
-The difference between two complementary angles is 85°. What is the measure of the larger angle?

Accepted Answer

A) 2.5° 
B) 5° 
C) 87.5° 
D) 132.5° 
A) 2.5° 
B) 5° 
C) 87.5° 
D) 132.5°

Question 10

Classify the triangle as acute, right, or obtuse and as equilateral, isosceles, or scalene.
-

Accepted Answer

A) Right, scalene 
B) Acute, isosceles 
C) Obtuse, scalene 
D) Obtuse, equilateral 
A) Right, scalene 
B) Acute, isosceles 
C) Obtuse, scalene 
D) Obtuse, equilateral

Question 11

There are various formulas that will generate Pythagorean triples. Use the specified formula and specified values to generate a Pythagorean triple.
-If m is an odd positive integer greater than 1, then $\left( \mathrm { m } , \frac { \mathrm { m } ^ { 2 } - 1 } { 2 } , \frac { \mathrm { m } ^ { 2 } + 1 } { 2 } \right)$ is a Pythagorean triple.
Use this method with the value $\mathrm { m } = 5$ to generate a Pythagorean triple.

Accepted Answer

A)  $( 5,8,18 )$ 
B)  $( 5,24,26 )$ 
C)  $( 6,12,13 )$ 
D)  $( 5,12,13 )$ 
A)  $( 5,8,18 )$ 
B)  $( 5,24,26 )$ 
C)  $( 6,12,13 )$ 
D)  $( 5,12,13 )$

Question 12

The alternate exterior angles of two parallel lines cut by a transversal always have the same angle
measure.

Accepted Answer

A) True 
 B)False

Question 13

Give the symbol that represents the portion of the line named and draw a figure showing just the portion named.
- 
$\text { Ray QS }$

Accepted Answer

A)    
B)    
C)    
D)   
A)    
B)    
C)    
D)

Question 14

Give the measure of the missing angle using the similar triangles below.
-$\angle B$

$\triangle \mathrm { ABC } \sim \triangle \mathrm { DEC } , \overline { \mathrm { AC } } = 8 \mathrm {~cm} , \angle \mathrm { E } = 58 ^ { \circ }$

Accepted Answer

A)  $8 \mathrm {~cm}$ 
B)  $92 ^ { \circ }$ 
C)  $58 ^ { \circ }$ 
D)  $30 ^ { \circ }$ 
A)  $8 \mathrm {~cm}$ 
B)  $92 ^ { \circ }$ 
C)  $58 ^ { \circ }$ 
D)  $30 ^ { \circ }$

Question 15

$\text { Refer to this figure to answer the question. Assume } \overleftrightarrow { \mathrm { CF } } \text { and } \overleftrightarrow { \mathrm { GJ } } \text { are parallel. }$

-$\text { What is the measure of } \angle \mathrm{DEF} \text { ? }$

Accepted Answer

A)  $90 ^ { \circ }$ 
B)  $0 ^ { \circ }$ 
C)  $120 ^ { \circ }$ 
D)  $180 ^ { \circ }$ 
A)  $90 ^ { \circ }$ 
B)  $0 ^ { \circ }$ 
C)  $120 ^ { \circ }$ 
D)  $180 ^ { \circ }$

Question 16

Find the measure of each unknown angle in triangle ABC.
- 
$\angle A = x ^ { \circ } , \angle B = 48 ^ { \circ } , \angle C = x ^ { \circ }$

Accepted Answer

A)  $\angle \mathrm { A } = \angle \mathrm { C } = 58 ^ { \circ }$ 
B)  $\angle A = \angle C = 48 ^ { \circ }$ 
C)  $\angle A = \angle C = 76 ^ { \circ }$ 
D)  $\angle A = \angle C = 66 ^ { \circ }$ 
A)  $\angle \mathrm { A } = \angle \mathrm { C } = 58 ^ { \circ }$ 
B)  $\angle A = \angle C = 48 ^ { \circ }$ 
C)  $\angle A = \angle C = 76 ^ { \circ }$ 
D)  $\angle A = \angle C = 66 ^ { \circ }$

Question 17

Solve the problem.
-A ladder is resting against a wall. The top of the ladder touches the wall at a height of 6 ft. Find the length of the ladder if the length is 2 ft more than its distance from the wall.

Accepted Answer

A) 10 ft 
B) 6 ft 
C) 8 ft 
D) 12 ft 
A) 10 ft 
B) 6 ft 
C) 8 ft 
D) 12 ft

Question 18

Give the symbol that represents the portion of the line named and draw a figure showing just the portion named.
- 
$\text { Ray QP }$

Accepted Answer

A)    
B)    
C)   
D)    
A)    
B)    
C)   
D)

Question 19

$\text { Refer to this figure to answer the question. Assume } \overleftrightarrow { \mathrm { CF } } \text { and } \overleftrightarrow { \mathrm { GJ } } \text { are parallel. }$

-What is the vertex of $\angle \mathrm { DEI }$ ?

Accepted Answer

A)  I 
B)  $\mathrm { E }$ 
C)  D 
A)  I 
B)  $\mathrm { E }$ 
C)  D

Question 20

Find the area.
- 
$a = 2.2 \mathrm {~m} , \mathrm {~b} = 7.4 \mathrm {~m}$

Accepted Answer

A)  $9.6 \mathrm {~m} ^ { 2 }$ 
B)  $16.28 \mathrm {~m} ^ { 2 }$ 
C)  $32.56 \mathrm {~m} ^ { 2 }$ 
D)  $8.8 \mathrm {~m} ^ { 2 }$ 
A)  $9.6 \mathrm {~m} ^ { 2 }$ 
B)  $16.28 \mathrm {~m} ^ { 2 }$ 
C)  $32.56 \mathrm {~m} ^ { 2 }$ 
D)  $8.8 \mathrm {~m} ^ { 2 }$

Based on the figure, specify the given set in a simpler way. -

Based on the figure, specify the given set in a simpler way. -

Based on the figure, specify the given set in a simpler way. -

a and b represent the two legs of a right triangle, while c represents the hypotenuse. Find the length of the unknown side. - $a = 10 \text { in., } b = 24 \text { in. }$

Refer to the given figure, an isosceles triangle with AB = AC. $Refer to the given figure, an isosceles triangle with AB = AC. -If \angle A measures 117 ^ { \circ } find the measure of \angle B .$ -If $\angle A$ measures $117 ^ { \circ }$ find the measure of $\angle B$ .

Solve the problem. -The difference between two complementary angles is 85°. What is the measure of the larger angle?

Classify the triangle as acute, right, or obtuse and as equilateral, isosceles, or scalene. -

The alternate exterior angles of two parallel lines cut by a transversal always have the same angle measure.

Give the symbol that represents the portion of the line named and draw a figure showing just the portion named. - $Give the symbol that represents the portion of the line named and draw a figure showing just the portion named. - \text { Ray QS }$ $\text { Ray QS }$

Find the measure of each unknown angle in triangle ABC. - $Find the measure of each unknown angle in triangle ABC. - \angle A = x ^ { \circ } , \angle B = 48 ^ { \circ } , \angle C = x ^ { \circ }$ $\angle A = x ^ { \circ } , \angle B = 48 ^ { \circ } , \angle C = x ^ { \circ }$

Solve the problem. -A ladder is resting against a wall. The top of the ladder touches the wall at a height of 6 ft. Find the length of the ladder if the length is 2 ft more than its distance from the wall.

Give the symbol that represents the portion of the line named and draw a figure showing just the portion named. - $Give the symbol that represents the portion of the line named and draw a figure showing just the portion named. - \text { Ray QP }$ $\text { Ray QP }$

Find the area. - $Find the area. - a = 2.2 \mathrm {~m} , \mathrm {~b} = 7.4 \mathrm {~m}$ $a = 2.2 \mathrm {~m} , \mathrm {~b} = 7.4 \mathrm {~m}$

The Art of Problem Solving

The Basic Concepts of Set Theory

Introduction to Logic

Numeration Systems

Number Theory

The Real Numbers and Their Representations

The Basic Concepts of Algebra

Graphs, Functions, and Systems of Equations and Inequalities

Counting Methods

Probability

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Personal Financial Management

Trigonometry Formerly

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Exam 9: Geometry

Based on the figure, specify the given set in a simpler way. -

Refer to the given figure, an isosceles triangle with AB = AC. -If the perimeter of △ABC=58 m\triangle \mathrm { ABC } = 58 \mathrm {~m}△ABC=58 m , and AB=25 m\mathrm { AB } = 25 \mathrm {~m}AB=25 m , what is the length BC\mathrm { BC }BC ?

Based on the figure, specify the given set in a simpler way. -

Use the properties of parallel lines to solve the problem. -Assume that m and n are parallel. Find the measures of angles A and B. ∠A=(4x−5)∘,∠B=(3x+26)∘\angle A=(4 x-5)^{\circ}, \angle B=(3 x+26)^{\circ}∠A=(4x−5)∘,∠B=(3x+26)∘

Based on the figure, specify the given set in a simpler way. -

a and b represent the two legs of a right triangle, while c represents the hypotenuse. Find the length of the unknown side. - a=10 in., b=24 in. a = 10 \text { in., } b = 24 \text { in. }a=10 in., b=24 in.

Refer to the given figure, an isosceles triangle with AB = AC. -If ∠A\angle A∠A measures 117∘117 ^ { \circ }117∘ find the measure of ∠B\angle B∠B .

Solve the problem. -The difference between two complementary angles is 85°. What is the measure of the larger angle?

Classify the triangle as acute, right, or obtuse and as equilateral, isosceles, or scalene. -

The alternate exterior angles of two parallel lines cut by a transversal always have the same angle measure.

Give the symbol that represents the portion of the line named and draw a figure showing just the portion named. - Ray QS \text { Ray QS } Ray QS

Find the measure of each unknown angle in triangle ABC. - ∠A=x∘,∠B=48∘,∠C=x∘\angle A = x ^ { \circ } , \angle B = 48 ^ { \circ } , \angle C = x ^ { \circ }∠A=x∘,∠B=48∘,∠C=x∘

Solve the problem. -A ladder is resting against a wall. The top of the ladder touches the wall at a height of 6 ft. Find the length of the ladder if the length is 2 ft more than its distance from the wall.

Give the symbol that represents the portion of the line named and draw a figure showing just the portion named. - Ray QP \text { Ray QP } Ray QP

Find the area. - a=2.2 m, b=7.4 ma = 2.2 \mathrm {~m} , \mathrm {~b} = 7.4 \mathrm {~m}a=2.2 m, b=7.4 m

The Art of Problem Solving

The Basic Concepts of Set Theory

Introduction to Logic

Numeration Systems

Number Theory

The Real Numbers and Their Representations

The Basic Concepts of Algebra

Graphs, Functions, and Systems of Equations and Inequalities

Counting Methods

Probability

Statistics

Personal Financial Management

Trigonometry Formerly

Graph Theory

Voting and Apportionment

Filters

a and b represent the two legs of a right triangle, while c represents the hypotenuse. Find the length of the unknown side. - $a = 10 \text { in., } b = 24 \text { in. }$

Refer to the given figure, an isosceles triangle with AB = AC. $Refer to the given figure, an isosceles triangle with AB = AC. -If \angle A measures 117 ^ { \circ } find the measure of \angle B .$ -If $\angle A$ measures $117 ^ { \circ }$ find the measure of $\angle B$ .

Give the symbol that represents the portion of the line named and draw a figure showing just the portion named. - $Give the symbol that represents the portion of the line named and draw a figure showing just the portion named. - \text { Ray QS }$ $\text { Ray QS }$

Find the measure of each unknown angle in triangle ABC. - $Find the measure of each unknown angle in triangle ABC. - \angle A = x ^ { \circ } , \angle B = 48 ^ { \circ } , \angle C = x ^ { \circ }$ $\angle A = x ^ { \circ } , \angle B = 48 ^ { \circ } , \angle C = x ^ { \circ }$

Give the symbol that represents the portion of the line named and draw a figure showing just the portion named. - $Give the symbol that represents the portion of the line named and draw a figure showing just the portion named. - \text { Ray QP }$ $\text { Ray QP }$

Find the area. - $Find the area. - a = 2.2 \mathrm {~m} , \mathrm {~b} = 7.4 \mathrm {~m}$ $a = 2.2 \mathrm {~m} , \mathrm {~b} = 7.4 \mathrm {~m}$