Question

question 5 of 10
based only on the information given in the diagram, which congruence
theorems or postulates could be given as reasons why ( \triangle l m n cong \triangle o p q ) ?
check all that apply.
a. aas
b. ll
c. sas
d. la
e. hl
f. asa

Explanation:

Step1: Analyze AAS

AAS (Angle - Angle - Side) states that if two angles and a non - included side of one triangle are congruent to two angles and the corresponding non - included side of another triangle, the triangles are congruent. In right - angled triangles $\triangle LMN$ and $\triangle OPQ$, we have two right angles ($\angle N=\angle Q = 90^{\circ}$), one pair of acute angles ($\angle L=\angle O$) and one pair of sides (the marked equal sides). So AAS can be used.

Step2: Analyze LL

LL (Leg - Leg) is a congruence theorem for right - angled triangles. If the legs of one right - angled triangle are congruent to the legs of another right - angled triangle, the triangles are congruent. Here, we have one leg (the marked equal sides) and the other leg (the sides adjacent to the right angles which are part of the angle - side relationships). So LL can be used.

Step3: Analyze LA

LA (Leg - Angle) is a congruence theorem for right - angled triangles. If a leg and an acute angle of one right - angled triangle are congruent to a leg and the corresponding acute angle of another right - angled triangle, the triangles are congruent. We have a leg (marked equal) and an acute angle ($\angle L=\angle O$). So LA can be used.

Answer:

A. AAS, B. LL, D. LA