Question 1

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

Accepted Answer

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

Question 2

If two lines are perpendicular, then they form vertical angles at their intersection which are always
acute.

Accepted Answer

A) True 
 B)False

Question 3

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

-Are $\angle$ CDA and $\angle G H D$ equal in measure?

Accepted Answer

A)  Yes 
B)  $\mathrm { No }$ 
A)  Yes 
B)  $\mathrm { No }$

Question 4

Find the area.
-A parallelogram with a base of 15 yd and a height of 22 yd

Accepted Answer

A)  $330 \mathrm { yd } ^ { 2 }$ 
B)  $484 \mathrm { yd } ^ { 2 }$ 
C)  $225 \mathrm { yd } ^ { 2 }$ 
D)  $328 \mathrm { yd } ^ { 2 }$ 
A)  $330 \mathrm { yd } ^ { 2 }$ 
B)  $484 \mathrm { yd } ^ { 2 }$ 
C)  $225 \mathrm { yd } ^ { 2 }$ 
D)  $328 \mathrm { yd } ^ { 2 }$

Question 5

Identify the curve as simple, closed, both, or neither.
-

Accepted Answer

A)  Simple 
B)  Both 
C)  Closed 
D)  Neither 
A)  Simple 
B)  Both 
C)  Closed 
D)  Neither

Question 6

Solve the problem.
-A triangle drawn on a map has sides of lengths 7.0 cm, 10 cm, and 14 cm. The shortest of the corresponding real-life distances is 105 km. Find the longest of the real-life distances. Round to the
Nearest unit.

Accepted Answer

A) 147 km 
B) 53 km 
C) 150 km 
D) 210 km 
A) 147 km 
B) 53 km 
C) 150 km 
D) 210 km

Question 7

For the given pair of similar triangles, name the corresponding side or angle in the other triangle.
-

Accepted Answer

A)    
B)   
C)  Cannot be determined 
D)   
A)    
B)   
C)  Cannot be determined 
D)

Question 8

Identify the curve as simple, closed, both, or neither.
-

Accepted Answer

A)  Neither 
B)  Simple 
C)  Closed 
D)  Both 
A)  Neither 
B)  Simple 
C)  Closed 
D)  Both

Question 9

Solve the problem.
-Find the measure of the indicated exterior angle.  
$\angle x=(200-4 n)^{\circ} \cdot \angle y=(5 n+61)^{\circ} \cdot \angle z=(n+9)^{\circ}$

Accepted Answer

A)  $144 ^ { \circ }$ 
B)  $122 ^ { \circ }$ 
C)  $148 ^ { \circ }$ 
D)  $128 ^ { \circ }$ 
A)  $144 ^ { \circ }$ 
B)  $122 ^ { \circ }$ 
C)  $148 ^ { \circ }$ 
D)  $128 ^ { \circ }$

Question 10

Find the measure of each unknown angle in triangle ABC.
- 
$\angle A = ( 37 - x ) ^ { \circ } , \angle B = ( 9 x - 27 ) ^ { \circ }$

Accepted Answer

A)  $\angle A = 31 ^ { \circ } , \angle B = 59 ^ { \circ }$ 
B)  $\angle A = \angle B = 45 ^ { \circ }$ 
C)  $\angle A = 27 ^ { \circ } , \angle B = 63 ^ { \circ }$ 
D)  $\angle \mathrm { A } = 21 ^ { \circ } , \angle \mathrm { B } = 69 ^ { \circ }$ 
A)  $\angle A = 31 ^ { \circ } , \angle B = 59 ^ { \circ }$ 
B)  $\angle A = \angle B = 45 ^ { \circ }$ 
C)  $\angle A = 27 ^ { \circ } , \angle B = 63 ^ { \circ }$ 
D)  $\angle \mathrm { A } = 21 ^ { \circ } , \angle \mathrm { B } = 69 ^ { \circ }$

Question 11

The two triangles below are similar. Find the unknown side lengths.
-

Accepted Answer

A)  $x = 20 ; y = 28$ 
B)  $x = 13.5 ; y = 18$ 
C)  $x = 11.25 ; y = 15.75$ 
D)  $x = 6 ; y = 12$ 
A)  $x = 20 ; y = 28$ 
B)  $x = 13.5 ; y = 18$ 
C)  $x = 11.25 ; y = 15.75$ 
D)  $x = 6 ; y = 12$

Question 12

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

Accepted Answer

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

Question 13

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

-Are $\angle \mathrm { GHD }$ and $\angle \mathrm { ADE }$ supplementary?

Accepted Answer

A)  $\mathrm { No }$ 
B)  Yes 
A)  $\mathrm { No }$ 
B)  Yes

Question 14

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

Accepted Answer

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

Question 15

Match the symbol with the answer choice that names the same set of points based on the given figure.
-

Accepted Answer

A)    
B)    
C)    
D)  None of these 
A)    
B)    
C)    
D)  None of these

Question 16

Solve the problem.
-A square with sides of length 20 is inscribed in a circle and circumscribed about another circle. What is the area between the circles?

Accepted Answer

A)  100 
B)  $100 \pi$ 
C)  $200 \pi$ 
D)  $10 \pi$ 
A)  100 
B)  $100 \pi$ 
C)  $200 \pi$ 
D)  $10 \pi$

Question 17

Solve the problem.
-The two circles have radii of 3 and 7 respectively. The distance between their centers is 36. What is x, the length of one of their common tangents?

Accepted Answer

A)  $\sqrt { 1354 }$ 
B)  $\sqrt { 1238 }$ 
C)  $\sqrt { 1287 }$ 
D)  $\sqrt { 1247 }$ 
A)  $\sqrt { 1354 }$ 
B)  $\sqrt { 1238 }$ 
C)  $\sqrt { 1287 }$ 
D)  $\sqrt { 1247 }$

Question 18

Find the measure of the angles.
- 
$\angle A=(5 x-48)^{\circ}, \angle B=(3 x+20)^{\circ}$

Accepted Answer

A)  $67.5 ^ { \circ }$ and $112.5 ^ { \circ }$ 
B)  $82 ^ { \circ }$ and $98 ^ { \circ }$ 
C)  $80 ^ { \circ }$ and $100 ^ { \circ }$ 
D)  $56 ^ { \circ }$ and $124 ^ { \circ }$ 
A)  $67.5 ^ { \circ }$ and $112.5 ^ { \circ }$ 
B)  $82 ^ { \circ }$ and $98 ^ { \circ }$ 
C)  $80 ^ { \circ }$ and $100 ^ { \circ }$ 
D)  $56 ^ { \circ }$ and $124 ^ { \circ }$

Question 19

Give the measure of the missing angle using the similar triangles below.
-$\angle \mathrm { A } ^ { \prime } \mathrm { C } ^ { \prime } \mathrm { B } ^ { \prime }$

$\triangle \mathrm { ABC } \sim \triangle \mathrm { A } ^ { \prime } \mathrm { B } ^ { \prime } \mathrm { C } ^ { \prime }$

Accepted Answer

A)  $\angle A ^ { \prime } C ^ { \prime } B ^ { \prime } = 132 ^ { \circ }$ 
B)  $\angle \mathrm { A } ^ { \prime } \mathrm { C } ^ { \prime } \mathrm { B } ^ { \prime } = 119 ^ { \circ }$ 
C)  $\angle A ^ { \prime } C ^ { \prime } B ^ { \prime } = 24 ^ { \circ }$ 
D)  $\angle \mathrm { A } ^ { \prime } \mathrm { C } ^ { \prime } \mathrm { B } ^ { \prime } = 37 ^ { \circ }$ 
A)  $\angle A ^ { \prime } C ^ { \prime } B ^ { \prime } = 132 ^ { \circ }$ 
B)  $\angle \mathrm { A } ^ { \prime } \mathrm { C } ^ { \prime } \mathrm { B } ^ { \prime } = 119 ^ { \circ }$ 
C)  $\angle A ^ { \prime } C ^ { \prime } B ^ { \prime } = 24 ^ { \circ }$ 
D)  $\angle \mathrm { A } ^ { \prime } \mathrm { C } ^ { \prime } \mathrm { B } ^ { \prime } = 37 ^ { \circ }$

Question 20

Decide whether the figure is convex or not convex.
-

Accepted Answer

A) Not convex 
B) Convex 
A) Not convex 
B) Convex

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

If two lines are perpendicular, then they form vertical angles at their intersection which are always acute.

Find the area. -A parallelogram with a base of 15 yd and a height of 22 yd

Identify the curve as simple, closed, both, or neither. -

Solve the problem. -A triangle drawn on a map has sides of lengths 7.0 cm, 10 cm, and 14 cm. The shortest of the corresponding real-life distances is 105 km. Find the longest of the real-life distances. Round to the Nearest unit.

For the given pair of similar triangles, name the corresponding side or angle in the other triangle. -

Identify the curve as simple, closed, both, or neither. -

Find the measure of each unknown angle in triangle ABC. - $Find the measure of each unknown angle in triangle ABC. - \angle A = ( 37 - x ) ^ { \circ } , \angle B = ( 9 x - 27 ) ^ { \circ }$ $\angle A = ( 37 - x ) ^ { \circ } , \angle B = ( 9 x - 27 ) ^ { \circ }$

The two triangles below are similar. Find the unknown side lengths. -

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

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

Match the symbol with the answer choice that names the same set of points based on the given figure. -

Solve the problem. -A square with sides of length 20 is inscribed in a circle and circumscribed about another circle. What is the area between the circles?

Solve the problem. -The two circles have radii of 3 and 7 respectively. The distance between their centers is 36. What is x, the length of one of their common tangents?

Find the measure of the angles. - $Find the measure of the angles. - \angle A=(5 x-48)^{\circ}, \angle B=(3 x+20)^{\circ}$ $\angle A=(5 x-48)^{\circ}, \angle B=(3 x+20)^{\circ}$

Decide whether the figure is convex or not convex. -

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

Exam 9: Geometry

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

If two lines are perpendicular, then they form vertical angles at their intersection which are always acute.

Find the area. -A parallelogram with a base of 15 yd and a height of 22 yd

Identify the curve as simple, closed, both, or neither. -

Solve the problem. -A triangle drawn on a map has sides of lengths 7.0 cm, 10 cm, and 14 cm. The shortest of the corresponding real-life distances is 105 km. Find the longest of the real-life distances. Round to the Nearest unit.

For the given pair of similar triangles, name the corresponding side or angle in the other triangle. -

Identify the curve as simple, closed, both, or neither. -

Solve the problem. -Find the measure of the indicated exterior angle. ∠x=(200−4n)∘⋅∠y=(5n+61)∘⋅∠z=(n+9)∘\angle x=(200-4 n)^{\circ} \cdot \angle y=(5 n+61)^{\circ} \cdot \angle z=(n+9)^{\circ}∠x=(200−4n)∘⋅∠y=(5n+61)∘⋅∠z=(n+9)∘

Find the measure of each unknown angle in triangle ABC. - ∠A=(37−x)∘,∠B=(9x−27)∘\angle A = ( 37 - x ) ^ { \circ } , \angle B = ( 9 x - 27 ) ^ { \circ }∠A=(37−x)∘,∠B=(9x−27)∘

The two triangles below are similar. Find the unknown side lengths. -

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

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

Match the symbol with the answer choice that names the same set of points based on the given figure. -

Solve the problem. -A square with sides of length 20 is inscribed in a circle and circumscribed about another circle. What is the area between the circles?

Solve the problem. -The two circles have radii of 3 and 7 respectively. The distance between their centers is 36. What is x, the length of one of their common tangents?

Find the measure of the angles. - ∠A=(5x−48)∘,∠B=(3x+20)∘\angle A=(5 x-48)^{\circ}, \angle B=(3 x+20)^{\circ}∠A=(5x−48)∘,∠B=(3x+20)∘

Decide whether the figure is convex or not convex. -

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

Find the measure of each unknown angle in triangle ABC. - $Find the measure of each unknown angle in triangle ABC. - \angle A = ( 37 - x ) ^ { \circ } , \angle B = ( 9 x - 27 ) ^ { \circ }$ $\angle A = ( 37 - x ) ^ { \circ } , \angle B = ( 9 x - 27 ) ^ { \circ }$

Find the measure of the angles. - $Find the measure of the angles. - \angle A=(5 x-48)^{\circ}, \angle B=(3 x+20)^{\circ}$ $\angle A=(5 x-48)^{\circ}, \angle B=(3 x+20)^{\circ}$