Question

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

5.
sss
sas
asa
aas
hl

Explanation:

Step1: Analyze SSS

SSS (Side - Side - Side) congruence states that if three sides of one triangle are equal to three sides of another triangle, the triangles are congruent. From the figure, we can assume the three pairs of corresponding sides are equal.

Step2: Analyze SAS

SAS (Side - Angle - Side) congruence requires two sides and the included angle to be equal. The vertical angles (the angles formed by the intersection of the two lines) are equal. And we have two pairs of equal sides.

Step3: Analyze ASA and AAS

For ASA (Angle - Side - Angle) and AAS (Angle - Angle - Side), we can also find the necessary angle - side - angle or angle - angle - side combinations. The vertical angles are equal, and from the side - side relationships, we can derive the angle - related congruence conditions.

Step4: Analyze HL

HL (Hypotenuse - Leg) is for right - angled triangles. There is no indication that these are right - angled triangles.

Answer:

SSS, SAS, ASA, AAS