Question 1

a and b represent the two legs of a right triangle, while c represents the hypotenuse. Find the length of the unknown side.
-

Accepted Answer

A)  $b = 7$ 
B)  $b = 10$ 
C)  $b = 9$ 
D)  $b = 8$ 
A)  $b = 7$ 
B)  $b = 10$ 
C)  $b = 9$ 
D)  $b = 8$

Question 2

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

Accepted Answer

A)  $x = 4.9 ; y = 3.9$ 
B)  $x = 1.60 ; y = 3.6$ 
C)  $x = 5.6 ; y = 3.9$ 
D)  $x = 4.9 ; y = 3.6$ 
A)  $x = 4.9 ; y = 3.9$ 
B)  $x = 1.60 ; y = 3.6$ 
C)  $x = 5.6 ; y = 3.9$ 
D)  $x = 4.9 ; y = 3.6$

Question 3

Provide a STATEMENT/REASON proof for the congruence.
- 
Given: $\mathrm { AC } = \mathrm { DC } , \angle \mathrm { BAC } = \angle \mathrm { EDC }$
Prove: $\triangle \mathrm { ACB } \cong \triangle \mathrm { DCE }$

Accepted Answer

\[\begin{array}{l}
\text { STATEMENTS|RE

Question 4

Decide whether the statement is true or false.
-If a quadrilateral is a parallelogram, then it must be a rhombus.

Accepted Answer

A) True 
 B)False

Question 5

If two lines intersect in more than one point, they must be the same line.

Accepted Answer

A) True 
 B)False

Question 6

Give the measure of the missing angle using the similar triangles below.
-$\angle E$
 
$\triangle \mathrm{ABC} \sim \triangle \mathrm{DEF}, \overline{\mathrm{AC}}=24 \mathrm{~cm}, \angle \mathrm{B}=113$

Accepted Answer

A)  $24 \mathrm{~cm}$ 
B)  $10^{\circ}$ 
C)  $57^{\circ}$ 
D)  $113^{\circ}$ 
A)  $24 \mathrm{~cm}$ 
B)  $10^{\circ}$ 
C)  $57^{\circ}$ 
D)  $113^{\circ}$

Question 7

Solve the problem.
-A square with sides of length 14 is inscribed in a circle and circumscribed about another circle. What is the area of the larger circle?

Accepted Answer

A)  $7 \pi$ 
B)  98 
C)  $49 \pi$ 
D)  $98 \pi$ 
A)  $7 \pi$ 
B)  98 
C)  $49 \pi$ 
D)  $98 \pi$

Question 8

a and b represent the two legs of a right triangle, while c represents the hypotenuse. Find the length of the unknown side.
-b = 21 cm, c = 29 cm

Accepted Answer

A) 21 cm 
B) a = 20 cm 
C) 22 = cm 
D) a = 19 cm 
A) 21 cm 
B) a = 20 cm 
C) 22 = cm 
D) a = 19 cm

Question 9

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

Accepted Answer

A)  $x = 44$ 
B)  $x = 36$ 
C)  $x = 55$ 
D)  $x = 41$ 
A)  $x = 44$ 
B)  $x = 36$ 
C)  $x = 55$ 
D)  $x = 41$

Question 10

Decide whether the figure is convex or not convex.
-

Accepted Answer

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

Question 11

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

Accepted Answer

A)  $\angle \mathrm { T }$ 
B)  $\angle R$ 
C)  $\angle S$ 
D)  $\angle C$ 
A)  $\angle \mathrm { T }$ 
B)  $\angle R$ 
C)  $\angle S$ 
D)  $\angle C$

Question 12

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 13

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

Accepted Answer

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

Question 14

a and b represent the two legs of a right triangle, while c represents the hypotenuse. Find the length of the unknown side.
-$\mathrm { a } = 18 \mathrm {~m} , \mathrm {~b} = 24 \mathrm {~m}$

Accepted Answer

A)  $\mathrm { c } = 16 \mathrm {~m}$ 
B)  $\mathrm { c } = 30 \mathrm {~m}$ 
C)  $\mathrm { c } = 29 \mathrm {~m}$ 
D)  $\mathrm { c } = 21 \mathrm {~m}$ 
A)  $\mathrm { c } = 16 \mathrm {~m}$ 
B)  $\mathrm { c } = 30 \mathrm {~m}$ 
C)  $\mathrm { c } = 29 \mathrm {~m}$ 
D)  $\mathrm { c } = 21 \mathrm {~m}$

Question 15

Solve the problem.
-Find the measure of the indicated exterior angle.  
$\angle X=(6 n-20)^{\circ}, \angle y=(5 n+0)^{\circ}, \angle Z=(172-n)^{\circ}$

Accepted Answer

A)  $84 ^ { \circ }$ 
B)  $164 ^ { \circ }$ 
C)  $156 ^ { \circ }$ 
D)  $174 ^ { \circ }$ 
A)  $84 ^ { \circ }$ 
B)  $164 ^ { \circ }$ 
C)  $156 ^ { \circ }$ 
D)  $174 ^ { \circ }$

Question 16

If a(n)right angle is broken up into two new angles, these two new angles are also right angles.

Accepted Answer

A) True 
 B)False

Question 17

Solve the problem.
-Find the measure of an angle if its supplement measures 72° less than 4 times its complement.

Accepted Answer

A) 36° 
B) 18° 
C) 76.5° 
D) 153° 
A) 36° 
B) 18° 
C) 76.5° 
D) 153°

Question 18

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

Accepted Answer

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

Question 19

Find the requested angle.
-Complement of 35°

Accepted Answer

A) 55° 
B) 70° 
C) 325° 
D) 145° 
A) 55° 
B) 70° 
C) 325° 
D) 145°

Question 20

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

Accepted Answer

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

a and b represent the two legs of a right triangle, while c represents the hypotenuse. Find the length of the unknown side. -

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

Decide whether the statement is true or false. -If a quadrilateral is a parallelogram, then it must be a rhombus.

If two lines intersect in more than one point, they must be the same line.

Solve the problem. -A square with sides of length 14 is inscribed in a circle and circumscribed about another circle. What is the area of the larger circle?

a and b represent the two legs of a right triangle, while c represents the hypotenuse. Find the length of the unknown side. -b = 21 cm, c = 29 cm

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

Decide whether the figure is convex or not convex. -

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

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. -

a and b represent the two legs of a right triangle, while c represents the hypotenuse. Find the length of the unknown side. - $\mathrm { a } = 18 \mathrm {~m} , \mathrm {~b} = 24 \mathrm {~m}$

Solve the problem. -Find the measure of the indicated exterior angle. $Solve the problem. -Find the measure of the indicated exterior angle. \angle X=(6 n-20)^{\circ}, \angle y=(5 n+0)^{\circ}, \angle Z=(172-n)^{\circ}$ $\angle X=(6 n-20)^{\circ}, \angle y=(5 n+0)^{\circ}, \angle Z=(172-n)^{\circ}$

If a(n)right angle is broken up into two new angles, these two new angles are also right angles.

Solve the problem. -Find the measure of an angle if its supplement measures 72° less than 4 times its complement.

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

Find the requested angle. -Complement of 35°

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

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

a and b represent the two legs of a right triangle, while c represents the hypotenuse. Find the length of the unknown side. -

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

Provide a STATEMENT/REASON proof for the congruence. - Given: AC=DC,∠BAC=∠EDC\mathrm { AC } = \mathrm { DC } , \angle \mathrm { BAC } = \angle \mathrm { EDC }AC=DC,∠BAC=∠EDC Prove: △ACB≅△DCE\triangle \mathrm { ACB } \cong \triangle \mathrm { DCE }△ACB≅△DCE

Decide whether the statement is true or false. -If a quadrilateral is a parallelogram, then it must be a rhombus.

If two lines intersect in more than one point, they must be the same line.

Give the measure of the missing angle using the similar triangles below. - ∠E\angle E∠E △ABC∼△DEF,AC‾=24 cm,∠B=113\triangle \mathrm{ABC} \sim \triangle \mathrm{DEF}, \overline{\mathrm{AC}}=24 \mathrm{~cm}, \angle \mathrm{B}=113△ABC∼△DEF,AC=24 cm,∠B=113

Solve the problem. -A square with sides of length 14 is inscribed in a circle and circumscribed about another circle. What is the area of the larger circle?

a and b represent the two legs of a right triangle, while c represents the hypotenuse. Find the length of the unknown side. -b = 21 cm, c = 29 cm

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

Decide whether the figure is convex or not convex. -

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

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. -

a and b represent the two legs of a right triangle, while c represents the hypotenuse. Find the length of the unknown side. - a=18 m, b=24 m\mathrm { a } = 18 \mathrm {~m} , \mathrm {~b} = 24 \mathrm {~m}a=18 m, b=24 m

Solve the problem. -Find the measure of the indicated exterior angle. ∠X=(6n−20)∘,∠y=(5n+0)∘,∠Z=(172−n)∘\angle X=(6 n-20)^{\circ}, \angle y=(5 n+0)^{\circ}, \angle Z=(172-n)^{\circ}∠X=(6n−20)∘,∠y=(5n+0)∘,∠Z=(172−n)∘

If a(n)right angle is broken up into two new angles, these two new angles are also right angles.

Solve the problem. -Find the measure of an angle if its supplement measures 72° less than 4 times its complement.

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

Find the requested angle. -Complement of 35°

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

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

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

a and b represent the two legs of a right triangle, while c represents the hypotenuse. Find the length of the unknown side. - $\mathrm { a } = 18 \mathrm {~m} , \mathrm {~b} = 24 \mathrm {~m}$

Solve the problem. -Find the measure of the indicated exterior angle. $Solve the problem. -Find the measure of the indicated exterior angle. \angle X=(6 n-20)^{\circ}, \angle y=(5 n+0)^{\circ}, \angle Z=(172-n)^{\circ}$ $\angle X=(6 n-20)^{\circ}, \angle y=(5 n+0)^{\circ}, \angle Z=(172-n)^{\circ}$

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