Question

example 5
ex5: which congruency theorem can be used to prove that these triangles are congruent?
aas sss sas hl asa
rewatch

Explanation:

Step1: Analyze given triangle info

We have two triangles. One pair of sides is marked equal (given by the tick marks), vertical angles are equal (since they are opposite angles formed by intersecting lines), and another pair of angles (the non - included angles with respect to the equal side) are marked equal.

Step2: Recall congruence theorems

• AAS (Angle - Angle - Side) congruence theorem states that if two angles and a non - included side of one triangle are congruent to the corresponding two angles and non - included side of another triangle, then the triangles are congruent.
• Let's check other theorems:
• SSS (Side - Side - Side) requires three pairs of equal sides, we only have one pair marked, so not SSS.
• SAS (Side - Angle - Side) requires two sides and the included angle, we don't have the included angle equal (we have vertical angles and another angle, not the included angle for the equal side), so not SAS.
• ASA (Angle - Side - Angle) requires two angles and the included side, we have two angles and a non - included side, so not ASA.
• HL (Hypotenuse - Leg) is for right triangles, and there's no indication these are right triangles.

So the AAS congruence theorem applies here.

Answer:

AAS