Question 1

The area of any regular polygon with length of apothem a and perimeter P is given by $A = \frac { 1 } { 2 } a P$ .

Accepted Answer

A) True 
 B)False

Question 2

The triangles shown in the illustration are congruent. The sides of the triangles are $a = 3$ , $b = 13$ , and $c = 3$ .  
So $d = 14$ .

Accepted Answer

A) True 
 B)False

Question 3

Find the volume of a rectangular solid with dimensions of 7 by 6 by 6 centimeters.

Accepted Answer

A)  $248 \mathrm {~cm} ^ { 3 }$ 
B)  $19 \mathrm {~cm} ^ { 3 }$ 
C)  $252 \mathrm {~cm} ^ { 3 }$ 
D)  $256 \mathrm {~cm} ^ { 3 }$ 
E)  none of these

Question 4

The circumference of a circle is 70 m. Find its radius. Use the rules for working with measurements.

Accepted Answer

A)  The radius is 4.7 m. 
B)  The radius is 11.1 m. 
C)  The radius is 5.6 m. 
D)  The radius is 22.3 m. 
E)  The radius is 44.6 m.

Question 5

Match between columns
                        Premises: parallelogram
rhombus
rectangle

Accepted Answer

The Answer of Close the Files and Read a Record is...

Question 6

In the figure below, $l _ { 1 }$  is parallel with $l _ { 2 }$ .
Find x , if $a = 5$ , $$b = 4$$  and $$c = 17$$ .

Accepted Answer

A)  $292 ^ { \circ }$ 
B)  $17 ^ { \circ }$ 
C)  $146 ^ { \circ }$ 
D)  $163 ^ { \circ }$ 
E)  none of these

Question 7

In the figure below, $a = 10$ , $b = 5$ , and  $c = 45$ .
What is the measure of angle y ?

Accepted Answer

A)  99 
B)  189 
C)  90 
D)  9 
E)  none of these

Question 8

Choose the correct word.
Any _____ different points determine exactly one line.

Accepted Answer

A)  two 
B)  three

Question 9

Find $\angle 2$  if  $$\angle 1 = 39 ^ { \circ }$$

Accepted Answer

A)  $51 ^ { \circ }$ 
B)  $39 ^ { \circ }$ 
C)  $52 ^ { \circ }$ 
D)  $40 ^ { \circ }$ 
E)  none of these

Question 10

FIGURE 1  
The right triangle ABC is shown in Figure 1. Find the length of the missing side by using the Pythagorean Theorem, if $a = 12$ ft and $b = 16$ ft. 
c = __________ ft

Accepted Answer

The answer of FIGURE 1  
The right triangle ABC...

Question 11

The angles of the triangles shown in the illustration are  $a = 60 ^ { \circ }$ , $b = 60 ^ { \circ }$ . The triangles are congruent because of what property?

Accepted Answer

A)  SAS property 
B)  ASA property 
C)  SSS property

Question 12

Refer to the figure above to find the length of segment $\overline { DA}$

Accepted Answer

A)  4 
B)  3 
C)  2 
D)  7

Question 13

The measures of two angles of ABC (shown in the illustration) are given. Find the measure of the third angle, if $m ( \angle A ) = 51.08 ^ { \circ }$  and $m ( \angle B ) = 56.46 ^ { \circ }$ .

Accepted Answer

A)  $71.46 ^ { \circ }$ 
B)  $72.46 ^ { \circ }$ 
C)  $82.47 ^ { \circ }$ 
D)  $72.57 ^ { \circ }$ 
E)  $72.36 ^ { \circ }$

Question 14

In isosceles triangle $R S T$ , $\overline { R S } \cong \overline { S T }$ . If $m \angle T = 2 ( x + 3 )$ and $m \angle S = 3 x$ , find the value of x .

Accepted Answer

A)  $x = 24$ 
B)  $x = 32$ 
C)  $x = 46$ 
D)  $x = 58$

Question 15

An __________ triangle has two sides of equal length .

Accepted Answer

The answer of An __________ triangle has two sides of equal length ....

Question 16

In the figure below, $A B \| C D$ . Are $\triangle A O B$  and $$\triangle C O D$$  similar triangles?

Accepted Answer

A)  Yes 
B)  No

Question 17

The north wall of a barn is a rectangle 60 feet high and 55 feet long. There are five windows in the wall, each 4 by 4 feet. If a gallon of paint will cover 400 square feet, how many gallons of paint must the painter buy to paint the wall?

Accepted Answer

A)  9 
B)  8 
C)  10 
D)  11 
E)  none of these

Question 18

Refer to the illustration. Find $C$  if $a = 4$  and $b = 3$ .

Accepted Answer

A)  5 
B)  $\sqrt { 60 }$ 
C)  $\sqrt { 18 }$ 
D)  $\sqrt { 17 }$ 
E)  7

Question 19

The lengths of the sides of different triangles are given below. Which is a right triangle?

Accepted Answer

A)  5, 12, 12 
B)  9, 7, 10 
C)  6, 13, 14 
D)  5, 12, 13 
E)  9, 7, 11

Question 20

Refer to the rectangle ABCD , shown below, where $m ( \angle 4 ) = 18 ^ { \circ }$ .

Accepted Answer

A)  $m ( \angle 1 ) = 72 ^ { \circ }$ , $m ( \angle 2 ) = 72 ^ { \circ }$  and $m ( \angle 3 ) = 18 ^ { \circ }$ 
B)  $m ( \angle 1 ) = 18 ^ { \circ }$ , $m ( \angle 2 ) = 72 ^ { \circ }$  and $m ( \angle 3 ) = 18 ^ { \circ }$ 
C)  $m ( \angle 1 ) = 72 ^ { \circ }$ , $m ( \angle 2 ) = 18 ^ { \circ }$  and $m ( \angle 3 ) = 72 ^ { \circ }$ 
D)  $m ( \angle 1 ) = 18 ^ { \circ }$ , $m ( \angle 2 ) = 18 ^ { \circ }$  and $m ( \angle 3 ) = 72 ^ { \circ }$

Exam 9: An Introduction to Geometry

The area of any regular polygon with length of apothem a and perimeter P is given by $A = \frac { 1 } { 2 } a P$ .

The triangles shown in the illustration are congruent. The sides of the triangles are $a = 3$ , $b = 13$ , and $c = 3$ . So $d = 14$ .

Find the volume of a rectangular solid with dimensions of 7 by 6 by 6 centimeters.

The circumference of a circle is 70 m. Find its radius. Use the rules for working with measurements.

In the figure below, $a = 10$ , $b = 5$ , and $c = 45$ . What is the measure of angle y ?

Choose the correct word. Any _____ different points determine exactly one line.

Find $\angle 2$ if $\angle 1 = 39 ^ { \circ }$ $Find \angle 2 if \angle 1 = 39 ^ { \circ } A) 51 ^ { \circ } B) 39 ^ { \circ } C) 52 ^ { \circ } D) 40 ^ { \circ } E) none of these$

FIGURE 1 The right triangle ABC is shown in Figure 1. Find the length of the missing side by using the Pythagorean Theorem, if $a = 12$ ft and $b = 16$ ft. c = __________ ft

$Refer to the figure above to find the length of segment \overline { DA} A) 4 B) 3 C) 2 D) 7$ Refer to the figure above to find the length of segment $\overline { DA}$

The measures of two angles of ABC (shown in the illustration) are given. Find the measure of the third angle, if $m ( \angle A ) = 51.08 ^ { \circ }$ and $m ( \angle B ) = 56.46 ^ { \circ }$ .

In isosceles triangle $R S T$ , $\overline { R S } \cong \overline { S T }$ . If $m \angle T = 2 ( x + 3 )$ and $m \angle S = 3 x$ , find the value of x .

An __________ triangle has two sides of equal length .

In the figure below, $A B \| C D$ . Are $\triangle A O B$ and $\triangle C O D$ similar triangles? $In the figure below, A B \| C D . Are \triangle A O B and \triangle C O D similar triangles? A) Yes B) No$

The north wall of a barn is a rectangle 60 feet high and 55 feet long. There are five windows in the wall, each 4 by 4 feet. If a gallon of paint will cover 400 square feet, how many gallons of paint must the painter buy to paint the wall?

Refer to the illustration. Find $C$ if $a = 4$ and $b = 3$ . $Refer to the illustration. Find C if a = 4 and b = 3 . A) 5 B) \sqrt { 60 } C) \sqrt { 18 } D) \sqrt { 17 } E) 7$

The lengths of the sides of different triangles are given below. Which is a right triangle?

Exam 9: An Introduction to Geometry

The area of any regular polygon with length of apothem a and perimeter P is given by A=12aPA = \frac { 1 } { 2 } a PA=21​aP .

The triangles shown in the illustration are congruent. The sides of the triangles are a=3a = 3a=3 , b=13b = 13b=13 , and c=3c = 3c=3 . So d=14d = 14d=14 .

Find the volume of a rectangular solid with dimensions of 7 by 6 by 6 centimeters.

The circumference of a circle is 70 m. Find its radius. Use the rules for working with measurements.

In the figure below, l1l _ { 1 }l1​ is parallel with l2l _ { 2 }l2​ . Find x , if a=5a = 5a=5 , b=4b = 4b=4 and c=17c = 17c=17 .

In the figure below, a=10a = 10a=10 , b=5b = 5b=5 , and c=45c = 45c=45 . What is the measure of angle y ?

Choose the correct word. Any _____ different points determine exactly one line.

Find ∠2\angle 2∠2 if ∠1=39∘\angle 1 = 39 ^ { \circ }∠1=39∘

FIGURE 1 The right triangle ABC is shown in Figure 1. Find the length of the missing side by using the Pythagorean Theorem, if a=12a = 12a=12 ft and b=16b = 16b=16 ft. c = __________ ft

The angles of the triangles shown in the illustration are a=60∘a = 60 ^ { \circ }a=60∘ , b=60∘b = 60 ^ { \circ }b=60∘ . The triangles are congruent because of what property?

Refer to the figure above to find the length of segment DA‾\overline { DA}DA

The measures of two angles of ABC (shown in the illustration) are given. Find the measure of the third angle, if m(∠A) =51.08∘m ( \angle A ) = 51.08 ^ { \circ }m(∠A) =51.08∘ and m(∠B) =56.46∘m ( \angle B ) = 56.46 ^ { \circ }m(∠B) =56.46∘ .

In isosceles triangle RSTR S TRST , RS‾≅ST‾\overline { R S } \cong \overline { S T }RS≅ST . If m∠T=2(x+3) m \angle T = 2 ( x + 3 ) m∠T=2(x+3) and m∠S=3xm \angle S = 3 xm∠S=3x , find the value of x .

An __________ triangle has two sides of equal length .

In the figure below, AB∥CDA B \| C DAB∥CD . Are △AOB\triangle A O B△AOB and △COD\triangle C O D△COD similar triangles?

The north wall of a barn is a rectangle 60 feet high and 55 feet long. There are five windows in the wall, each 4 by 4 feet. If a gallon of paint will cover 400 square feet, how many gallons of paint must the painter buy to paint the wall?

Refer to the illustration. Find CCC if a=4a = 4a=4 and b=3b = 3b=3 .

The lengths of the sides of different triangles are given below. Which is a right triangle?

Refer to the rectangle ABCD , shown below, where m(∠4) =18∘m ( \angle 4 ) = 18 ^ { \circ }m(∠4) =18∘ .

The area of any regular polygon with length of apothem a and perimeter P is given by $A = \frac { 1 } { 2 } a P$ .

The triangles shown in the illustration are congruent. The sides of the triangles are $a = 3$ , $b = 13$ , and $c = 3$ . So $d = 14$ .

In the figure below, $a = 10$ , $b = 5$ , and $c = 45$ . What is the measure of angle y ?

Find $\angle 2$ if $\angle 1 = 39 ^ { \circ }$ $Find \angle 2 if \angle 1 = 39 ^ { \circ } A) 51 ^ { \circ } B) 39 ^ { \circ } C) 52 ^ { \circ } D) 40 ^ { \circ } E) none of these$

FIGURE 1 The right triangle ABC is shown in Figure 1. Find the length of the missing side by using the Pythagorean Theorem, if $a = 12$ ft and $b = 16$ ft. c = __________ ft

$Refer to the figure above to find the length of segment \overline { DA} A) 4 B) 3 C) 2 D) 7$ Refer to the figure above to find the length of segment $\overline { DA}$

The measures of two angles of ABC (shown in the illustration) are given. Find the measure of the third angle, if $m ( \angle A ) = 51.08 ^ { \circ }$ and $m ( \angle B ) = 56.46 ^ { \circ }$ .

In isosceles triangle $R S T$ , $\overline { R S } \cong \overline { S T }$ . If $m \angle T = 2 ( x + 3 )$ and $m \angle S = 3 x$ , find the value of x .

In the figure below, $A B \| C D$ . Are $\triangle A O B$ and $\triangle C O D$ similar triangles? $In the figure below, A B \| C D . Are \triangle A O B and \triangle C O D similar triangles? A) Yes B) No$

Refer to the illustration. Find $C$ if $a = 4$ and $b = 3$ . $Refer to the illustration. Find C if a = 4 and b = 3 . A) 5 B) \sqrt { 60 } C) \sqrt { 18 } D) \sqrt { 17 } E) 7$