Question 1

Find the missing side lengths in the triangle. Give the exact answer and then an approximation to two decimal places, when appropriate.

Accepted Answer

A)  $x = 10 \sqrt { 3 } \approx 17.35 , h = 20$ 
B)  $x = 10 \sqrt { 3 } \approx 17.32 , h = 20$ 
C)  $x = 20 , h = 10 \sqrt { 3 } \approx 17.32$ 
D)  $x = 21 , h = 10 \sqrt { 3 } \approx 17.35$ 
E)  $x = 10 \sqrt { 3 } \approx 17.32 , h = 21$ 
A)  $x = 10 \sqrt { 3 } \approx 17.35 , h = 20$ 
B)  $x = 10 \sqrt { 3 } \approx 17.32 , h = 20$ 
C)  $x = 20 , h = 10 \sqrt { 3 } \approx 17.32$ 
D)  $x = 21 , h = 10 \sqrt { 3 } \approx 17.35$ 
E)  $x = 10 \sqrt { 3 } \approx 17.32 , h = 21$

Question 2

Find the area of a regular hexagon whose sides measure 6 inches each.

Accepted Answer

A)  $9 \sqrt { 3 } \mathrm { in } ^ { 2 }$ 
B)  $9 \sqrt { 2 } \mathrm { in } ^ { 2 }$ 
C)  $54 \sqrt { 3 } \mathrm { in } ^ { 2 }$ 
D)  $54 \sqrt { 2 } \mathrm { in } ^ { 2 }$ 
A)  $9 \sqrt { 3 } \mathrm { in } ^ { 2 }$ 
B)  $9 \sqrt { 2 } \mathrm { in } ^ { 2 }$ 
C)  $54 \sqrt { 3 } \mathrm { in } ^ { 2 }$ 
D)  $54 \sqrt { 2 } \mathrm { in } ^ { 2 }$

Question 3

A man places a mirror on the ground and sees the reflection of the top of a building, as shown in the illustration. $b = 36$ , $c = 252$ , and $h = 28$ .

Accepted Answer

A)  32 
B)  $\frac { 1 } { 6 }$ 
C)  $\frac { 578 } { 3 }$ 
D)  4 
E)  none of these 
A)  32 
B)  $\frac { 1 } { 6 }$ 
C)  $\frac { 578 } { 3 }$ 
D)  4 
E)  none of these

Question 4

Fill in the blanks.
The ________ AB , written as $\overline { A B }$ , is the part of a line that consists of points A and B and all points in between.
A _______ is the part of a line that begins at some point (say, A ) and continues forever in one direction.

Accepted Answer

A)  line segment, line 
B)  line, ray 
C)  line, line segment 
D)  line segment, ray 
A)  line segment, line 
B)  line, ray 
C)  line, line segment 
D)  line segment, ray

Question 5

Find the area of the shaded part of the figure if $a = 18$ , $$b = 5$$ .

Accepted Answer

A)  90 
B)  180 
C)  45 
D)  14 
E)  none of these 
A)  90 
B)  180 
C)  45 
D)  14 
E)  none of these

Question 6

Are the two triangles shown in the illustration congruent if $a = 48$ ? Why?

Accepted Answer

A)  yes, SAS 
B)  yes, ASA 
C)  yes, AAA 
D)  yes, SSS 
E)  no 
A)  yes, SAS 
B)  yes, ASA 
C)  yes, AAA 
D)  yes, SSS 
E)  no

Question 7

Estimate the area of the sail on the windsurfing board.   
__________ $\mathrm { ft } ^ { 2 }$

Accepted Answer

The answer of Estimate the area of the sail on...

Question 8

A triangle with three sides of equal length is called a(n) __________ triangle.

Accepted Answer

The answer of A triangle with three sides of equal length is called a(n)...

Question 9

Refer to the illustration. Find $b$  if $a = 8$  and $c = 10$ .

Accepted Answer

A)  2 
B)  $\sqrt { 18 }$ 
C)  $\sqrt { 10 }$ 
D)  6 
E)  $\sqrt { 514 }$ 
A)  2 
B)  $\sqrt { 18 }$ 
C)  $\sqrt { 10 }$ 
D)  6 
E)  $\sqrt { 514 }$

Question 10

Choose case when the triangles are similar.

Accepted Answer

A)  $\angle A = 35 ^ { \circ }$ , $\angle B = 62 ^ { \circ }$ , $\angle N = 62 ^ { \circ }$ 
B)  $\angle A = 35 ^ { \circ }$ , $\angle M = 35 ^ { \circ }$ , $A B = 99$ , $A C = 110$ , $M N = 117$ , $M K = 130$ 
C)  $\angle C = 83 ^ { \circ }$ , $\angle K = 83 ^ { \circ }$ , $B C = 55$ , $A C = 110$ , $N K = 68$ , $M K = 130$ 
D)  $\angle B = 83 ^ { \circ }$ , $B C = 55$ , $A C = 110$ , $M K = 130$ 
A)  $\angle A = 35 ^ { \circ }$ , $\angle B = 62 ^ { \circ }$ , $\angle N = 62 ^ { \circ }$ 
B)  $\angle A = 35 ^ { \circ }$ , $\angle M = 35 ^ { \circ }$ , $A B = 99$ , $A C = 110$ , $M N = 117$ , $M K = 130$ 
C)  $\angle C = 83 ^ { \circ }$ , $\angle K = 83 ^ { \circ }$ , $B C = 55$ , $A C = 110$ , $N K = 68$ , $M K = 130$ 
D)  $\angle B = 83 ^ { \circ }$ , $B C = 55$ , $A C = 110$ , $M K = 130$

Question 11

Find the total area of the shaded figure.  
The side of the square is equal to 12. Use $\pi = 3.1416$ .

Accepted Answer

A)  1,614.9 
B)  113.1 
C)  115.7 
D)  30.9 
E)  none of these 
A)  1,614.9 
B)  113.1 
C)  115.7 
D)  30.9 
E)  none of these

Question 12

Use the dimensions in the illustration to find w , the width of the river, if $a = 16$ , $b = 20$ , and $$c = 80$$ .

Accepted Answer

A)  64 
B)  80 
C)  $\frac { 1 } { 27 }$ 
D)  $\frac { 36 } { 5 }$ 
E)  none of these 
A)  64 
B)  80 
C)  $\frac { 1 } { 27 }$ 
D)  $\frac { 36 } { 5 }$ 
E)  none of these

Question 13

Name anlge 3 in three appropiate ways.

Accepted Answer

A)  ∠ CBE ; ∠ EBC ; ∠ B; 
B)  ∠1;∠ ABD ;∠ DBA 
C)  ∠3; ∠ CBE ; ∠ EBC 
D)  ∠ ABD ; ∠ DBA ; ∠ B 
A)  ∠ CBE ; ∠ EBC ; ∠ B; 
B)  ∠1;∠ ABD ;∠ DBA 
C)  ∠3; ∠ CBE ; ∠ EBC 
D)  ∠ ABD ; ∠ DBA ; ∠ B

Question 14

Find the supplement of a  $46 ^ { \circ }$  angle.

Accepted Answer

A)  $136 ^ { \circ }$ 
B)  $134 ^ { \circ }$ 
C)  $46 ^ { \circ }$ 
D)  $44 ^ { \circ }$ 
E)  $314 ^ { \circ }$ 
A)  $136 ^ { \circ }$ 
B)  $134 ^ { \circ }$ 
C)  $46 ^ { \circ }$ 
D)  $44 ^ { \circ }$ 
E)  $314 ^ { \circ }$

Question 15

Find the perimeter and the area of the quadrilateral.   
A) A = 48 m 2
B) A = 46 m 2
C) A = 64 m 2
D) P = 32 m
E) P = 28 m
F) P = 16 m

Accepted Answer

Question 16

The tree in the illustration casts a shadow $c = 6$  feet long, while a person $a = 6$  feet tall casts a shadow $b = 4$  feet long. 
Find the height of the tree.

Accepted Answer

A)  $\frac { 3 } { 12 }$ 
B)  15 
C)  $\frac { 1 } { 9 }$ 
D)  9 
E)  none of these 
A)  $\frac { 3 } { 12 }$ 
B)  15 
C)  $\frac { 1 } { 9 }$ 
D)  9 
E)  none of these

Question 17

In the figure below, angle $a = 34 ^ { \circ }$ and angle $b = 68 ^ { \circ }$ .
What is the measure of angle x ?

Accepted Answer

A)  34 
B)  40.5 
C)  27.5 
D)  129.5 
E)  none of these 
A)  34 
B)  40.5 
C)  27.5 
D)  129.5 
E)  none of these

Question 18

What are two lines in the same plane called?

Accepted Answer

A)  perpendicular 
B)  intersecting 
C)  transversal 
D)  coplanar 
E)  parallel 
A)  perpendicular 
B)  intersecting 
C)  transversal 
D)  coplanar 
E)  parallel

Question 19

In isosceles triangle RST , $\overline { R S } \cong \overline { S T }$ . If $R S = 2 x + 3$ , $R T = x$ , and the perimeter of $\triangle R S T$ is 36, find the value of x .

Accepted Answer

A)  $x = 5.5$ 
B)  $x = 6$ 
C)  $x = 6.5$ 
D)  None of These 
A)  $x = 5.5$ 
B)  $x = 6$ 
C)  $x = 6.5$ 
D)  None of These

Question 20

What are two lines which intersect and form right angles called?

Accepted Answer

A)  perpendicular 
B)  straight 
C)  intersecting 
D)  parallel 
E)  none of these 
A)  perpendicular 
B)  straight 
C)  intersecting 
D)  parallel 
E)  none of these

Find the missing side lengths in the triangle. Give the exact answer and then an approximation to two decimal places, when appropriate.

Find the area of a regular hexagon whose sides measure 6 inches each.

A man places a mirror on the ground and sees the reflection of the top of a building, as shown in the illustration. $b = 36$ , $c = 252$ , and $h = 28$ .

Fill in the blanks. The __ AB , written as $\overline { A B }$ , is the part of a line that consists of points A and B and all points in between. A _ is the part of a line that begins at some point (say, A ) and continues forever in one direction.

Find the area of the shaded part of the figure if $a = 18$ , $b = 5$ .

Are the two triangles shown in the illustration congruent if $a = 48$ ? Why?

Estimate the area of the sail on the windsurfing board. $Estimate the area of the sail on the windsurfing board. \mathrm { ft } ^ { 2 }$ $\mathrm { ft } ^ { 2 }$

A triangle with three sides of equal length is called a(n) __________ triangle.

Refer to the illustration. Find $b$ if $a = 8$ and $c = 10$ .

Choose case when the triangles are similar.

Find the total area of the shaded figure. $Find the total area of the shaded figure. The side of the square is equal to 12. Use \pi = 3.1416 .$ The side of the square is equal to 12. Use $\pi = 3.1416$ .

Use the dimensions in the illustration to find w , the width of the river, if $a = 16$ , $b = 20$ , and $c = 80$ .

Name anlge 3 in three appropiate ways.

Find the supplement of a $46 ^ { \circ }$ angle.

Find the perimeter and the area of the quadrilateral. A) A = 48 m ² B) A = 46 m ² C) A = 64 m ² D) P = 32 m E) P = 28 m F) P = 16 m

The tree in the illustration casts a shadow $c = 6$ feet long, while a person $a = 6$ feet tall casts a shadow $b = 4$ feet long. Find the height of the tree.

In the figure below, angle $a = 34 ^ { \circ }$ and angle $b = 68 ^ { \circ }$ . What is the measure of angle x ? $In the figure below, angle a = 34 ^ { \circ } and angle b = 68 ^ { \circ } . What is the measure of angle x ?$

What are two lines in the same plane called?

In isosceles triangle RST , $\overline { R S } \cong \overline { S T }$ . If $R S = 2 x + 3$ , $R T = x$ , and the perimeter of $\triangle R S T$ is 36, find the value of x .

What are two lines which intersect and form right angles called?

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Exam 9: An Introduction to Geometry

Find the missing side lengths in the triangle. Give the exact answer and then an approximation to two decimal places, when appropriate.

Find the area of a regular hexagon whose sides measure 6 inches each.

A man places a mirror on the ground and sees the reflection of the top of a building, as shown in the illustration. b=36b = 36b=36 , c=252c = 252c=252 , and h=28h = 28h=28 .

Fill in the blanks. The ________ AB , written as AB‾\overline { A B }AB , is the part of a line that consists of points A and B and all points in between. A _______ is the part of a line that begins at some point (say, A ) and continues forever in one direction.

Find the area of the shaded part of the figure if a=18a = 18a=18 , b=5b = 5b=5 .

Are the two triangles shown in the illustration congruent if a=48a = 48a=48 ? Why?

Estimate the area of the sail on the windsurfing board. __________ ft2\mathrm { ft } ^ { 2 }ft2

A triangle with three sides of equal length is called a(n) __________ triangle.

Refer to the illustration. Find bbb if a=8a = 8a=8 and c=10c = 10c=10 .

Choose case when the triangles are similar.

Find the total area of the shaded figure. The side of the square is equal to 12. Use π=3.1416\pi = 3.1416π=3.1416 .

Use the dimensions in the illustration to find w , the width of the river, if a=16a = 16a=16 , b=20b = 20b=20 , and c=80c = 80c=80 .

Name anlge 3 in three appropiate ways.

Find the supplement of a 46∘46 ^ { \circ }46∘ angle.

Find the perimeter and the area of the quadrilateral. A) A = 48 m 2 B) A = 46 m 2 C) A = 64 m 2 D) P = 32 m E) P = 28 m F) P = 16 m

The tree in the illustration casts a shadow c=6c = 6c=6 feet long, while a person a=6a = 6a=6 feet tall casts a shadow b=4b = 4b=4 feet long. Find the height of the tree.

In the figure below, angle a=34∘a = 34 ^ { \circ }a=34∘ and angle b=68∘b = 68 ^ { \circ }b=68∘ . What is the measure of angle x ?

What are two lines in the same plane called?

In isosceles triangle RST , RS‾≅ST‾\overline { R S } \cong \overline { S T }RS≅ST . If RS=2x+3R S = 2 x + 3RS=2x+3 , RT=xR T = xRT=x , and the perimeter of △RST\triangle R S T△RST is 36, find the value of x .

What are two lines which intersect and form right angles called?

Whole Numbers

The Integers

Fractions and Mixed Numbers

Decimals

Ratio, Proportion, and Measurement

Percent

Graphs, Statistics, and Probability

An Introduction to Algebra

Filters

A man places a mirror on the ground and sees the reflection of the top of a building, as shown in the illustration. $b = 36$ , $c = 252$ , and $h = 28$ .

Fill in the blanks. The __ AB , written as $\overline { A B }$ , is the part of a line that consists of points A and B and all points in between. A _ is the part of a line that begins at some point (say, A ) and continues forever in one direction.

Find the area of the shaded part of the figure if $a = 18$ , $b = 5$ .

Are the two triangles shown in the illustration congruent if $a = 48$ ? Why?

Estimate the area of the sail on the windsurfing board. $Estimate the area of the sail on the windsurfing board. \mathrm { ft } ^ { 2 }$ $\mathrm { ft } ^ { 2 }$

Refer to the illustration. Find $b$ if $a = 8$ and $c = 10$ .

Find the total area of the shaded figure. $Find the total area of the shaded figure. The side of the square is equal to 12. Use \pi = 3.1416 .$ The side of the square is equal to 12. Use $\pi = 3.1416$ .

Use the dimensions in the illustration to find w , the width of the river, if $a = 16$ , $b = 20$ , and $c = 80$ .

Find the supplement of a $46 ^ { \circ }$ angle.

Find the perimeter and the area of the quadrilateral. A) A = 48 m ² B) A = 46 m ² C) A = 64 m ² D) P = 32 m E) P = 28 m F) P = 16 m

The tree in the illustration casts a shadow $c = 6$ feet long, while a person $a = 6$ feet tall casts a shadow $b = 4$ feet long. Find the height of the tree.

In the figure below, angle $a = 34 ^ { \circ }$ and angle $b = 68 ^ { \circ }$ . What is the measure of angle x ? $In the figure below, angle a = 34 ^ { \circ } and angle b = 68 ^ { \circ } . What is the measure of angle x ?$

In isosceles triangle RST , $\overline { R S } \cong \overline { S T }$ . If $R S = 2 x + 3$ , $R T = x$ , and the perimeter of $\triangle R S T$ is 36, find the value of x .