Question

based only on the information given in the diagram, which congruence theorems or postulates could be given as reasons why △lmn≅△opq? check all that apply. a. la b. hl c. aas d. ll e. asa f. sas

Explanation:

Step1: Identify right - angled triangles

The two triangles $\triangle LMN$ and $\triangle OPQ$ are right - angled triangles as $\angle N=\angle Q = 90^{\circ}$.

Step2: Analyze congruence postulates

• LA (Leg - Angle): If one leg and an acute angle of a right - angled triangle are congruent to one leg and an acute angle of another right - angled triangle, the triangles are congruent. From the diagram, we can assume we have such a case.
• LL (Leg - Leg): If the two legs of one right - angled triangle are congruent to the two legs of another right - angled triangle, the triangles are congruent. The tick marks on the legs suggest this could be the case.

We don't have information about hypotenuses for HL, and not enough information for AAS, ASA or SAS based on the diagram alone.

Answer:

A. LA
D. LL