Question

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

Explanation:

Step1: Identify right - angled triangles

The given triangles $\triangle DEF$ and $\triangle KLM$ are right - angled triangles as indicated by the right - angle symbols at $\angle D$ and $\angle K$.

Step2: Analyze side - side congruence

We can see that one leg of $\triangle DEF$ is congruent to one leg of $\triangle KLM$ (the single - ticked sides) and the other leg of $\triangle DEF$ is congruent to the other leg of $\triangle KLM$ (the double - ticked sides). This satisfies the LL (Leg - Leg) congruence for right - angled triangles. Also, we have two sides and the included right - angle congruent, which satisfies the SAS (Side - Angle - Side) congruence.

Step3: Analyze angle - side congruence

Since we have right - angles, a pair of legs congruent and we can consider the right - angle as an included angle, we can also use the LA (Leg - Angle) congruence for right - angled triangles.

Answer:

C. LA
D. SAS
F. LL