AnswersOC27 MATH COLL LIB ARTS-1207350-S1-Maguire-DAquinoCongruent and Similar Triangles in the Coordinate Plane

Congruent and Similar Triangles in the Coordinate Plane Answers

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1
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Which of the following are congruent? Select four correct answers.

A
ΔSTV and ΔUTV
B
ST and TV
C
∠STV and ∠SVT
D
UV and SV
E
∠U and ∠S
F
∠TVU and ∠SVT
2
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Which did you include in your answer?

A
Find corresponding sides.
B
Use the SSS congruence theorem.
C
Corresponding sides are the same length.
D
Use the SSS similarity theorem.
E
The proportion is 1.
3

Which are the coordinates of the vertices of a triangle congruent to ΔPQR?

A
(0,5), (2,10), (0,10)
B
(9,−3), (9,0), (4,0)
C
(4,3), (−4,8), (−4,3)
D
(2.5,−4), (0,0), (0,−4)
4

Which statements are true? Check all that apply.The corresponding sides of similar triangles have proportional lengths.The corresponding sides of congruent triangles have the same lengths.The corresponding angles of similar triangles have different measures.If corresponding sides of two triangles are not the same length, the triangles are not similar.If corresponding sides of two triangles are not the same length, the triangles are not congruent.

A
The corresponding sides of similar triangles have proportional lengths.
B
The corresponding sides of congruent triangles have the same lengths.
C
The corresponding angles of similar triangles have different measures.
D
If corresponding sides of two triangles are not the same length, the triangles are not similar.
E
If corresponding sides of two triangles are not the same length, the triangles are not congruent.
5

Consider one triangle whose sides measure [image 1] units, [image 2] units, and 2 units. Consider another triangle whose sides measure 2 units, [image 3] units, and [image 1] units. Are these triangles congruent, similar, or both? Explain your answer.

Question illustration
Answer:

The triangles are both congruent and similar. Their corresponding side lengths are the same (3/2, 5/2, and 2), so they are congruent by SSS; congruent triangles are also similar.

6

The sides LM, MN, and LN of ΔLMN have sides of length , 15, and 15, respectively. Which triangle is similar to ΔLMN using the SSS similarity theorem?

Question illustration
A
Option
B
Option
C
Option
D
Option
7

What additional information is needed to prove that using the SAS congruence theorem?

Question illustration
A
the measure of ∠C and ∠D
B
the side lengths of AC and DF
C
the measure of ∠F and ∠A
D
the side lengths of AB and DB
8

Daniel claims that any two right triangles can be proven to be similar by the SAS similarity theorem because both have right angles that are congruent.What is his mistake?

Answer:

SAS requires two pairs of corresponding sides to be proportional as well as the included angles to be congruent. Congruent right angles alone are not enough, so two right triangles are not necessarily similar.

9

What can be concluded about triangles RST and VTU?

A
The triangles are congruent and similar with a proportional relationship of 1.
B
The triangles are congruent but not similar.
C
The triangles are similar but not congruent.
D
There is not enough information to determine if the triangles are congruent or similar.
10

Which did you include in your answer? Check all that apply.

A
The corresponding sides must also be in proportion.
B
He did not satisfy all the requirements of the theorem.

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