Question

1. determine which method if any can prove the triangles are congruent. there is more than one, check all that apply

sss
sas
asa
aas
hl

Explanation:

Step1: Analyze vertical angles

Vertical angles are equal. So, one pair of angles is congruent.

Step2: Check given right angles

Both triangles have a right - angle (\(90^{\circ}\)).

Step3: Check side - side relationship

The two triangles have a pair of equal sides (marked as equal in the figure).

For AAS (Angle - Angle - Side):
We have two angles (right - angle and vertical angle) and a non - included side (the marked equal side).

For ASA (Angle - Side - Angle):
If we consider the vertical angle as the included angle between the right - angle and the side (marked equal), it also works.

Answer:

ASA, AAS