Title: Chapter 4 Free Response
Course: quiz duplicate error

[Image]. List the six pairs of congruent corresponding parts.
[Image]

Based on the given information, can you conclude that [Image]? Explain.
Given: [Image], [Image], and [Image]

Can you conclude the triangles are congruent? Justify your answer.
[Image]

Complete the proof by providing the missing reasons.

Given: [Image], [Image] [Image]
Prove: [Image]
[Image]

Statement | Reason
1. [Image], [Image], and [Image] | 1. Given
2. [Image] are right angles | 2. Definition of perpendicular segments
3. [Image] | 3. ?
4. [Image] | 4. ?
5. [Image] | 5. ?

Complete the statement [Image]. Explain why it is true.
[Image]

Determine which triangles in the figure are congruent by AAS.
[Image]

Explain how you can use SSS, SAS, ASA, or AAS with CPCTC to show that BA=DA.

Given: [Image] [Image]
Prove: [Image]
[Image]

Explain how you can use SSS, SAS, ASA, or AAS with CPCTC to prove that [Image].
[Image]

For [Image] and [Image], [Image], [Image], and [Image]. Explain how you can prove [Image] by ASA.

For the two quadrilaterals below, [Image] [Image] [Image] and [Image] Complete this congruence statement for the two quadrilaterals.
[Image] ___?___

[Image]

Given that [Image], what else do you need to prove that [Image]? Outline a proof that uses the needed information.
[Image]

Guy wires of equal length anchor a vertical post to the flat ground. The guy wires are attached to the post at the same height. Explain why the guy wires reach the ground at the same distance from the base of the post.

In the figure, [Image], [Image], and [Image]. Prove that [Image].

[Image]

Is [Image] by HL? If so, name the legs that allow the use of HL.
[Image]

Is there enough information to prove the two triangles congruent by AAS? If yes, write the congruence statement and explain. If no, write not possible and tell what other information you would need.

Given: [Image]
[Image]

Is there enough information to prove the two triangles congruent? If yes, write the congruence statement and name the postulate you would use. If no, write not possible and tell what other information you would need.
[Image]

It appears from the name of the HL Theorem that you actually need to know that only two parts of two triangles are congruent in order to prove two triangles congruent. Is this the case?

Name a pair of triangles in the figure and state whether they are congruent by SSS, SAS, ASA, AAS, or HL.
Given: [Image], [Image]
[Image]

When you open a stepladder, you use a brace on each side of the ladder to lock the legs in place. Explain why the triangles formed on each side by the legs and the ground ( [Image] in the diagram) are congruent.

[Image]

Explain why [Image].
Given: [Image] and [Image]
[Image]

Write a proof.

Given: [Image], [Image] and [Image]
Prove: [Image]
[Image]

Write a two-column proof to show that [Image]
Given: [Image] [Image] and [Image]
[Image]

Explain why given the following information, $$BA \simeq ED$$
Given: [Image] and [Image]
Prove: [Image]
[Image]

Explain why given the following information lets you show that BC=CD.
Given: [Image]
Prove: [Image]
[Image]

Is there enough information to prove that PS is congruent to RS? If yes, explain how you would prove that the two segments are congruent. If no, write not possible and tell what other information you would need.
[Image]

Explain how you can use SSS, SAS, ASA, or AAS to show that $$\Delta \$$ ABC = $$\Delta \$$ ADC.

Given: [Image] [Image]
Prove: $$\Delta \$$ ABC = $$\Delta \$$ ADC
[Image]