Question

unit exam - congruent triangles
which of the following relationships proves why
△acd and △ecb are congruent?
hl
aas
sas
asa

Explanation:

1. First, identify the given information from the diagram: We can see that two sides of \(\triangle ACD\) and \(\triangle ECB\) are marked as equal (the tick marks indicate congruent sides), and the included angle at \(C\) is common (or congruent) to both triangles.
2. Recall the triangle congruence criteria:

• HL (Hypotenuse - Leg) is for right - angled triangles, and there's no indication these are right - angled.
• AAS (Angle - Angle - Side) requires two angles and a non - included side, but we have two sides and an included angle here.
• SAS (Side - Angle - Side) states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, the triangles are congruent. Since we have two congruent sides (from the tick marks) and the included angle at \(C\) is congruent (common angle), the SAS criterion applies.
• ASA (Angle - Side - Angle) requires two angles and the included side, which is not the case here as we have two sides and the included angle.

Answer:

SAS