Question

if two triangles have three congruent, corresponding angles, what additional information is needed to prove that the triangles are congruent?
one pair of corresponding angles must be congruent
sample response: 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.
what did you include in your response? check all that apply.
☐ congruent, corresponding side lengths are needed.
☐ the triangles need corresponding, congruent sides to be congruent.
☐ once congruent sides are known, the asa or aas congruence theorems or rigid transformations can be used to prove congruence.

Explanation:

1. For the first option: To prove triangle congruence with three congruent angles, we need at least one set of congruent corresponding sides. So this statement is correct.
2. For the second option: The triangles do need corresponding, congruent sides to be congruent (along with the three congruent angles) as per congruence theorems like ASA, AAS. So this is correct.
3. For the third option: Once we have congruent sides along with the three congruent angles, we can use ASA (Angle - Side - Angle), AAS (Angle - Angle - Side) congruence theorems or rigid transformations (which preserve shape and size) to prove the triangles are congruent. So this is correct.

Answer:

• $\boldsymbol{\square}$ Congruent, corresponding side lengths are needed. (Checked)
• $\boldsymbol{\square}$ The triangles need corresponding, congruent sides to be congruent. (Checked)
• $\boldsymbol{\square}$ Once congruent sides are known, the ASA or AAS congruence theorems or rigid transformations can be used to prove congruence. (Checked)