Triangle Congruence: ASA and AAS

Question 1

Can you conclude that triangle GHF is congruent to triangle GJK? Explain.

Revolt · Accepted Answer

D: not enough information given

Question 2

Are the triangles congruent? If so, how do you know?

Revolt · Accepted Answer

C: yes, because of ASA or AAS

Question 3

✔ LNMLON LMN NLM

Revolt · Accepted Answer

A: LNM

Question 4

Isabelle proves that the triangles are congruent by using the parallel lines to determine a second set of angles are congruent. What statement and reason could she have used?

Revolt · Accepted Answer

C: ∠ABC ≅ ∠DCB; alternate interior angles of parallel lines are congruent

Question 5

Determine the rigid transformations that will map ΔABC to ΔXYZ.

Revolt · Accepted Answer

D: Translate vertex X to vertex A; rotate ΔXYZ to align the sides and angles.

Question 6

What additional information could be used to prove that ΔXYZ ≅ ΔFEG using ASA or AAS? Check all that apply.∠Z ≅ ∠G and XZ ≅ FG∠Z ≅ ∠G and ∠Y ≅ ∠EXZ ≅ FG and ZY ≅ GEXY ≅ EF and ZY ≅ FG∠Z ≅ ∠G and XY ≅ FE

Revolt · Accepted Answer

A: ∠Z ≅ ∠G and XZ ≅ FG; E: ∠Z ≅ ∠G and XY ≅ FE

Question 7

If two triangles have three congruent, corresponding angles, what additional information is needed to prove that the triangles are congruent?

Revolt · Accepted Answer

To prove that two triangles with three congruent, corresponding angles are congruent, you would need to have at least one set of corresponding sides that are also congruent. You could then use ASA or AAS congruence theorems or rigid transformations to prove congruence.

Question 8

During geometry class, students are told that ΔTSR ≅ ΔUSV. Marcus states that ΔTSR is mapped to ΔUSV by performing a rotation about point S. Sam states that ΔTSR is mapped to ΔUSV by a reflection across the line that goes through point S. Determine if either student is correct.

Revolt · Accepted Answer

A: Marcus is correct.

Question 9

Explain how the angle-angle-side congruence theorem is an extension of the angle-side-angle congruence theorem. Be sure to discuss the information you would need for each theorem.

Revolt · Accepted Answer

The interior angle measures of a triangle add up to 180 degrees. Thus, if you are given angle-angle-side, you can solve for the third angle measure and essentially have angle-side-angle because the given side will now be the included side.

Question 10

LNM LON LMN ✔ MLN

Revolt · Accepted Answer

D: MLN

Triangle Congruence: ASA and AAS Answers

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