Question 1

Find the measures of the indicated sides, angles, or diagonals of the given parallelogram.
-$P M=31$ and $L P=37$. Find the length of each diagonal.

A) $\mathrm{LN}=37, \mathrm{MO}=31$
B) $\mathrm{LN}=74, \mathrm{MO}=62$
C) $\mathrm{LN}=62, \mathrm{MO}=74$
D) $\mathrm{LN}=\mathrm{MO}=68$

Accepted Answer

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Question 2

Find the measures of the indicated sides, angles, or diagonals of the given parallelogram.
-Find $m \angle A, m \angle B$, and $m \angle C$.

A)  
B)  
C) 
D)

Accepted Answer

The answer of Find the measures of the indicated sides,...

Question 3

Find the measures of the indicated sides, angles, or diagonals of the given parallelogram.
-Find $m \angle S, m \angle T, m \angle V$.

A)  
B)  
C)  
D)

Accepted Answer

The answer of Find the measures of the indicated sides,...

Question 4

Find the measures of the indicated sides, angles, or diagonals of the given parallelogram.
-Find $\mathrm{m} \angle \mathrm{W}, \mathrm{m} \angle \mathrm{Y}, \mathrm{m} \angle \mathrm{Z}$.

A)  
B) 
C)  
D)

Accepted Answer

The answer of Find the measures of the indicated sides,...

Question 5

Provide an appropriate response.
-For the pair of similar triangles, name the corresponding sides and angles.

A) $\angle \mathrm{A} \leftrightarrow \mathrm{D}, \angle \mathrm{B} \leftrightarrow \mathrm{F}, \angle \mathrm{C} \leftrightarrow \mathrm{X} ; \overline{\mathrm{AB}} \leftrightarrow \overline{\mathrm{FD}}, \overline{\mathrm{AC}} \leftrightarrow \overline{\mathrm{DX}}, \overline{\mathrm{BC}} \leftarrow \overline{\mathrm{FX}}$
B) $\angle \mathrm{A} \leftrightarrow \mathrm{F}, \angle \mathrm{B} \leftrightarrow \mathrm{D}, \angle \mathrm{C} \leftrightarrow \mathrm{X} ; \overline{\mathrm{AB}} \leftrightarrow \overline{\mathrm{FD}}, \overline{\mathrm{AC}} \leftrightarrow \overline{\mathrm{FX}}, \overline{\mathrm{BC}} \leftrightarrow \overline{\mathrm{DX}}$
C) $\angle \mathrm{A} \leftrightarrow \mathrm{X}, \angle \mathrm{B} \leftrightarrow \mathrm{D}, \angle \mathrm{C} \leftrightarrow \mathrm{F} ; \overline{\mathrm{AB}} \leftrightarrow \overline{\mathrm{DX}}, \overline{\mathrm{AC}} \leftrightarrow \overline{\mathrm{FX}}, \overline{\mathrm{BC}} \leftarrow \overline{\mathrm{FD}}$

Accepted Answer

The answer of Provide an appropriate response.
-For the pair of...

Question 6

Provide an appropriate response.
-For the pair of similar triangles, name the corresponding sides and angles.

A) $\angle \mathrm{A} \leftrightarrow \mathrm{Z}, \angle \mathrm{B} \leftrightarrow \mathrm{M}, \angle \mathrm{C} \leftrightarrow \mathrm{L} ; \overline{\mathrm{AB}} \leftrightarrow \overline{\mathrm{ZM}}, \overline{\mathrm{AC}} \leftrightarrow \overline{\mathrm{ZL}}, \overline{\mathrm{BC}} \leftrightarrow \overline{\mathrm{ML}}$
B) $\angle \mathrm{A} \leftrightarrow \mathrm{Z}, \angle \mathrm{B} \leftrightarrow \mathrm{L}, \angle \mathrm{C} \leftrightarrow \mathrm{M} ; \overline{\mathrm{AB}} \leftrightarrow \overline{\mathrm{ZL}}, \overline{\mathrm{AC}} \leftrightarrow \overline{\mathrm{ZM}}, \overline{\mathrm{BC}} \leftrightarrow \overline{\mathrm{ML}}$
C) $\angle \mathrm{A} \leftrightarrow \mathrm{L}, \angle \mathrm{B} \leftrightarrow \mathrm{M}, \angle \mathrm{C} \leftrightarrow Z ; \overline{\mathrm{AB}} \leftrightarrow \overline{\mathrm{ML}}, \overline{\mathrm{AC}} \leftrightarrow \overline{\mathrm{ZL}}, \overline{\mathrm{BC}} \leftarrow \overline{\mathrm{ZM}}$
D) $\angle \mathrm{A} \leftrightarrow \mathrm{M}, \angle \mathrm{B} \leftrightarrow \mathrm{Z}, \angle \mathrm{C} \leftrightarrow \mathrm{L} ; \overline{\mathrm{AB}} \leftrightarrow \overline{\mathrm{ZM}}, \overline{\mathrm{AC}} \leftrightarrow \overline{\mathrm{ML}}, \overline{\mathrm{BC}} \leftrightarrow \overline{\mathrm{ZL}}$

Accepted Answer

The answer of Provide an appropriate response.
-For the pair of...

Question 7

Provide an appropriate response.
-For the pair of similar triangles, name the congruent angles and proportional sides.
$\triangle \mathrm{ABC} \sim \triangle \mathrm{MNO}$
A) $\angle \mathrm{A} \cong \angle \mathrm{O}, \angle \mathrm{B} \cong \triangle \mathrm{N}, \angle \mathrm{C} \cong \angle \mathrm{M} ; \frac{\mathrm{AB}}{\mathrm{NO}}=\frac{\mathrm{AC}}{\mathrm{MO}}=\frac{\mathrm{BC}}{\mathrm{MN}}$
B) $\angle \mathrm{A} \cong \triangle \mathrm{M}, \angle \mathrm{B} \cong \angle \mathrm{N}, \angle \mathrm{C} \cong \angle \mathrm{O} ; \frac{\mathrm{AB}}{\mathrm{MN}}=\frac{\mathrm{AC}}{\mathrm{MO}}=\frac{\mathrm{BC}}{\mathrm{NO}}$
C) $\angle \mathrm{A} \cong \triangle \mathrm{N}, \angle \mathrm{B} \cong \triangle \mathrm{M}, \angle \mathrm{C} \cong \angle \mathrm{O} ; \frac{\mathrm{AB}}{\mathrm{MN}}=\frac{\mathrm{AC}}{\mathrm{NO}}=\frac{\mathrm{BC}}{\mathrm{MO}}$
D) $\angle \mathrm{A} \cong \triangle \mathrm{M}, \angle \mathrm{B} \cong \angle \mathrm{O}, \angle \mathrm{C} \cong \angle \mathrm{N} ; \frac{\mathrm{AB}}{\mathrm{MO}}=\frac{\mathrm{AC}}{\mathrm{MN}}=\frac{\mathrm{BC}}{\mathrm{NO}}$

Accepted Answer

When two triangles are similar, their corresponding angles are congruent, and the lengths of their corresponding sides are proportional. The correct correspondence between $\triangle ABC$ and $\triangle MNO$ is that $\angle A$ corresponds to $\angle M$, $\angle B$ to $\angle N$, and $\angle C$ to $\angle O$, making the sides proportional as stated in choice B.

Question 8

Provide an appropriate response.
-For the pair of similar triangles, name the congruent angles and proportional sides.
$\triangle \mathrm{ABC} \sim \triangle \mathrm{ZML}$
A) $\angle \mathrm{A} \cong \triangle \mathrm{M}, \angle \mathrm{B} \cong \angle \mathrm{Z}, \angle \mathrm{C} \cong \triangle \mathrm{L} ; \frac{\mathrm{AB}}{\mathrm{ZM}}=\frac{\mathrm{AC}}{\mathrm{ML}}=\frac{\mathrm{BC}}{\mathrm{ZL}}$
B) $\angle \mathrm{A} \cong \triangle \mathrm{L}, \angle \mathrm{B} \cong \triangle \mathrm{M}, \angle \mathrm{C} \cong \angle \mathrm{Z} ; \frac{\mathrm{AB}}{\mathrm{ML}}=\frac{\mathrm{AC}}{\mathrm{ZL}}=\frac{\mathrm{BC}}{\mathrm{ZM}}$
C) $\angle \mathrm{A} \cong \angle \mathrm{Z}, \angle \mathrm{B} \cong \triangle \mathrm{M}, \angle \mathrm{C} \cong \triangle \mathrm{L} ; \frac{\mathrm{AB}}{\mathrm{ZM}}=\frac{\mathrm{AC}}{\mathrm{ZL}}=\frac{\mathrm{BC}}{\mathrm{ML}}$
D) $\angle \mathrm{A} \cong \angle \mathrm{Z}, \angle \mathrm{B} \cong \angle \mathrm{L}, \angle \mathrm{C} \cong \triangle \mathrm{M} ; \frac{\mathrm{AB}}{\mathrm{ZL}}=\frac{\mathrm{AC}}{\mathrm{ZM}}=\frac{\mathrm{BC}}{\mathrm{ML}}$

Accepted Answer

When two triangles are similar, their corresponding angles are congruent, and the lengths of their corresponding sides are proportional. The correct correspondence between the angles of $\triangle ABC$ and $\triangle ZML$ is $\angle A \cong \angle Z$, $\angle B \cong \angle M$, and $\angle C \cong \angle L$, which matches the description in option C. This also means the sides opposite these angles are proportional as described in option C.

Question 9

Provide an appropriate response.
-Name the proportional sides in these similar triangles.

A) $\frac{\mathrm{AB}}{\mathrm{SR}}=\frac{\mathrm{AC}}{\mathrm{RM}}=\frac{\mathrm{BC}}{\mathrm{SM}}$
B) $\frac{\mathrm{AB}}{\mathrm{SR}}=\frac{\mathrm{AC}}{\mathrm{SM}}=\frac{\mathrm{BC}}{\mathrm{RM}}$
C) $\frac{\mathrm{AB}}{\mathrm{SM}}=\frac{\mathrm{AC}}{\mathrm{SR}}=\frac{\mathrm{BC}}{\mathrm{RM}}$
D) $\frac{\mathrm{AB}}{\mathrm{SM}}=\frac{\mathrm{AC}}{\mathrm{RM}}=\frac{\mathrm{BC}}{\mathrm{SR}}$

Accepted Answer

The answer of Provide an appropriate response.
-Name the proportional sides...

Question 10

Provide an appropriate response.
-Name the proportional sides in these similar triangles.

A) $\frac{\mathrm{AB}}{\mathrm{RS}}=\frac{\mathrm{AC}}{\mathrm{SM}}=\frac{\mathrm{BC}}{\mathrm{RM}}$
B) $\frac{\mathrm{AB}}{\mathrm{RM}}=\frac{\mathrm{AC}}{\mathrm{SM}}=\frac{\mathrm{BC}}{\mathrm{RS}}$
C) $\frac{A B}{R M}=\frac{A C}{R S}=\frac{B C}{S M}$
D) $\frac{\mathrm{AB}}{\mathrm{RS}}=\frac{\mathrm{AC}}{\mathrm{RM}}=\frac{\mathrm{BC}}{\mathrm{SM}}$

Accepted Answer

The answer of Provide an appropriate response.
-Name the proportional sides...

Question 11

Find the missing length.
-If $\triangle \mathrm{ABC} \sim \triangle \mathrm{XYZ}$, find $B C$.

A) 10
B) 21
C) 7
D) 14

Accepted Answer

The answer of Find the missing length.
-If \(\triangle \mathrm{ABC} \sim...

Question 12

Find the missing length.
-If $\triangle \mathrm{ABC} \sim \triangle \mathrm{XYZ}$, find $A C$.

A) 5
B) 15
C) 11
D) 10

Accepted Answer

The answer of Find the missing length.
-If \(\triangle \mathrm{ABC} \sim...

Question 13

Find the missing length.
-If $\overline{\mathrm{PQ}} \| \overline{\mathrm{RS}}$, find $\mathrm{PQ}$.

A) 36
B) 44
C) 41
D) 55

Accepted Answer

The answer of Find the missing length.
-If $\overline{\mathrm{PQ}} \| \overline{\mathrm{RS}}$,...

Question 14

Solve the problem.
-How high is a tree that casts a 39 - $\mathrm{ft}$ shadow at the same time that a 36 - $\mathrm{ft}$ flagpole casts a 95 - $\mathrm{ft}$ shadow? Round your answer to the nearest tenth.
A) $102.9 \mathrm{ft}$
B) $14.8 \mathrm{ft}$
C) $101.4 \mathrm{ft}$
D) $13.3 \mathrm{ft}$

Accepted Answer

Using similar triangles, the height of the tree can be found using the proportion: $\frac{\text{height of tree}}{39} = \frac{36}{95}$. Solving for the height of the tree gives approximately 14.8 ft.

Question 15

Solve the problem.
-When a $2 \frac{1}{2}$-ft fence post casts a 1 - $\mathrm{ft}$ shadow, how long is the shadow cast by a $10-\mathrm{ft}$ tree?
A) $4 \frac{1}{2} \mathrm{ft}$
B) $5 \frac{1}{4} \mathrm{ft}$
C) $4 \mathrm{ft}$
D) $5 \mathrm{ft}$

Accepted Answer

The answer of Solve the problem.
-When a $2 \frac{1}{2}$-ft fence...

Question 16

Solve the problem.
-Find the height of the building. Assume that the height of the person is $5 \mathrm{ft}$.

A) $540.8 \mathrm{ft}$
B) $112 \mathrm{ft}$
C) $41.6 \mathrm{ft}$
D) $80 \mathrm{ft}$

Accepted Answer

The answer of Solve the problem.
-Find the height of the...

Question 17

Solve the problem.
-Find the length, $L$, of the lake. Assume that the two triangles are similar.

A) $350 \mathrm{~m}$
B) $23.3 \mathrm{~m}$
C) $210 \mathrm{~m}$
D) $4900 \mathrm{~m}$

Accepted Answer

The answer of Solve the problem.
-Find the length, $L$, of...

Quiz 6: Geometry

Find the measures of the indicated sides, angles, or diagonals of the given parallelogram. -Find $m \angle A, m \angle B$ , and $m \angle C$ . $Find the measures of the indicated sides, angles, or diagonals of the given parallelogram. -Find m \angle A, m \angle B , and m \angle C . A) B) C) D)$

Find the measures of the indicated sides, angles, or diagonals of the given parallelogram. -Find $m \angle S, m \angle T, m \angle V$ . $Find the measures of the indicated sides, angles, or diagonals of the given parallelogram. -Find m \angle S, m \angle T, m \angle V . A) B) C) D)$

Provide an appropriate response. -For the pair of similar triangles, name the congruent angles and proportional sides. $\triangle \mathrm{ABC} \sim \triangle \mathrm{MNO}$

Provide an appropriate response. -For the pair of similar triangles, name the congruent angles and proportional sides. $\triangle \mathrm{ABC} \sim \triangle \mathrm{ZML}$

Find the missing length. -If $\triangle \mathrm{ABC} \sim \triangle \mathrm{XYZ}$ , find $B C$ . $Find the missing length. -If \triangle \mathrm{ABC} \sim \triangle \mathrm{XYZ} , find B C . A) 10 B) 21 C) 7 D) 14$

Find the missing length. -If $\triangle \mathrm{ABC} \sim \triangle \mathrm{XYZ}$ , find $A C$ . $Find the missing length. -If \triangle \mathrm{ABC} \sim \triangle \mathrm{XYZ} , find A C . A) 5 B) 15 C) 11 D) 10$

Find the missing length. -If $\overline{\mathrm{PQ}} \| \overline{\mathrm{RS}}$ , find $\mathrm{PQ}$ . $Find the missing length. -If \overline{\mathrm{PQ}} \| \overline{\mathrm{RS}} , find \mathrm{PQ} . A) 36 B) 44 C) 41 D) 55$

Solve the problem. -How high is a tree that casts a 39 - $\mathrm{ft}$ shadow at the same time that a 36 - $\mathrm{ft}$ flagpole casts a 95 - $\mathrm{ft}$ shadow? Round your answer to the nearest tenth.

Solve the problem. -When a $2 \frac{1}{2}$ -ft fence post casts a 1 - $\mathrm{ft}$ shadow, how long is the shadow cast by a $10-\mathrm{ft}$ tree?

Solve the problem. -Find the height of the building. Assume that the height of the person is $5 \mathrm{ft}$ . $Solve the problem. -Find the height of the building. Assume that the height of the person is 5 \mathrm{ft} . A) 540.8 \mathrm{ft} B) 112 \mathrm{ft} C) 41.6 \mathrm{ft} D) 80 \mathrm{ft}$

Solve the problem. -Find the length, $L$ , of the lake. Assume that the two triangles are similar. $Solve the problem. -Find the length, L , of the lake. Assume that the two triangles are similar. A) 350 \mathrm{~m} B) 23.3 \mathrm{~m} C) 210 \mathrm{~m} D) 4900 \mathrm{~m}$

Quiz 6: Geometry

Find the measures of the indicated sides, angles, or diagonals of the given parallelogram. - PM=31P M=31PM=31 and LP=37L P=37LP=37 . Find the length of each diagonal.

Find the measures of the indicated sides, angles, or diagonals of the given parallelogram. -Find m∠A,m∠Bm \angle A, m \angle Bm∠A,m∠B , and m∠Cm \angle Cm∠C .

Find the measures of the indicated sides, angles, or diagonals of the given parallelogram. -Find m∠S,m∠T,m∠Vm \angle S, m \angle T, m \angle Vm∠S,m∠T,m∠V .

Find the measures of the indicated sides, angles, or diagonals of the given parallelogram. -Find m∠W,m∠Y,m∠Z\mathrm{m} \angle \mathrm{W}, \mathrm{m} \angle \mathrm{Y}, \mathrm{m} \angle \mathrm{Z}m∠W,m∠Y,m∠Z .

Provide an appropriate response. -For the pair of similar triangles, name the corresponding sides and angles.

Provide an appropriate response. -For the pair of similar triangles, name the corresponding sides and angles.

Provide an appropriate response. -For the pair of similar triangles, name the congruent angles and proportional sides. △ABC∼△MNO\triangle \mathrm{ABC} \sim \triangle \mathrm{MNO}△ABC∼△MNO

Provide an appropriate response. -For the pair of similar triangles, name the congruent angles and proportional sides. △ABC∼△ZML\triangle \mathrm{ABC} \sim \triangle \mathrm{ZML}△ABC∼△ZML

Provide an appropriate response. -Name the proportional sides in these similar triangles.

Provide an appropriate response. -Name the proportional sides in these similar triangles.

Find the missing length. -If △ABC∼△XYZ\triangle \mathrm{ABC} \sim \triangle \mathrm{XYZ}△ABC∼△XYZ , find BCB CBC .

Find the missing length. -If △ABC∼△XYZ\triangle \mathrm{ABC} \sim \triangle \mathrm{XYZ}△ABC∼△XYZ , find ACA CAC .

Find the missing length. -If PQ‾∥RS‾\overline{\mathrm{PQ}} \| \overline{\mathrm{RS}}PQ​∥RS , find PQ\mathrm{PQ}PQ .

Solve the problem. -How high is a tree that casts a 39 - ft\mathrm{ft}ft shadow at the same time that a 36 - ft\mathrm{ft}ft flagpole casts a 95 - ft\mathrm{ft}ft shadow? Round your answer to the nearest tenth.

Solve the problem. -When a 2122 \frac{1}{2}221​ -ft fence post casts a 1 - ft\mathrm{ft}ft shadow, how long is the shadow cast by a 10−ft10-\mathrm{ft}10−ft tree?

Solve the problem. -Find the height of the building. Assume that the height of the person is 5ft5 \mathrm{ft}5ft .

Solve the problem. -Find the length, LLL , of the lake. Assume that the two triangles are similar.

Find the measures of the indicated sides, angles, or diagonals of the given parallelogram. -Find $m \angle A, m \angle B$ , and $m \angle C$ . $Find the measures of the indicated sides, angles, or diagonals of the given parallelogram. -Find m \angle A, m \angle B , and m \angle C . A) B) C) D)$

Find the measures of the indicated sides, angles, or diagonals of the given parallelogram. -Find $m \angle S, m \angle T, m \angle V$ . $Find the measures of the indicated sides, angles, or diagonals of the given parallelogram. -Find m \angle S, m \angle T, m \angle V . A) B) C) D)$

Provide an appropriate response. -For the pair of similar triangles, name the congruent angles and proportional sides. $\triangle \mathrm{ABC} \sim \triangle \mathrm{MNO}$

Provide an appropriate response. -For the pair of similar triangles, name the congruent angles and proportional sides. $\triangle \mathrm{ABC} \sim \triangle \mathrm{ZML}$

Find the missing length. -If $\triangle \mathrm{ABC} \sim \triangle \mathrm{XYZ}$ , find $B C$ . $Find the missing length. -If \triangle \mathrm{ABC} \sim \triangle \mathrm{XYZ} , find B C . A) 10 B) 21 C) 7 D) 14$

Find the missing length. -If $\triangle \mathrm{ABC} \sim \triangle \mathrm{XYZ}$ , find $A C$ . $Find the missing length. -If \triangle \mathrm{ABC} \sim \triangle \mathrm{XYZ} , find A C . A) 5 B) 15 C) 11 D) 10$

Find the missing length. -If $\overline{\mathrm{PQ}} \| \overline{\mathrm{RS}}$ , find $\mathrm{PQ}$ . $Find the missing length. -If \overline{\mathrm{PQ}} \| \overline{\mathrm{RS}} , find \mathrm{PQ} . A) 36 B) 44 C) 41 D) 55$

Solve the problem. -How high is a tree that casts a 39 - $\mathrm{ft}$ shadow at the same time that a 36 - $\mathrm{ft}$ flagpole casts a 95 - $\mathrm{ft}$ shadow? Round your answer to the nearest tenth.

Solve the problem. -When a $2 \frac{1}{2}$ -ft fence post casts a 1 - $\mathrm{ft}$ shadow, how long is the shadow cast by a $10-\mathrm{ft}$ tree?

Solve the problem. -Find the height of the building. Assume that the height of the person is $5 \mathrm{ft}$ . $Solve the problem. -Find the height of the building. Assume that the height of the person is 5 \mathrm{ft} . A) 540.8 \mathrm{ft} B) 112 \mathrm{ft} C) 41.6 \mathrm{ft} D) 80 \mathrm{ft}$

Solve the problem. -Find the length, $L$ , of the lake. Assume that the two triangles are similar. $Solve the problem. -Find the length, L , of the lake. Assume that the two triangles are similar. A) 350 \mathrm{~m} B) 23.3 \mathrm{~m} C) 210 \mathrm{~m} D) 4900 \mathrm{~m}$