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question 2
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can you prove these triangles are congruent? if so, how?
select one:
a. yes, by sss.
b. yes, by asa.
c. no, there is not enough information.
d. yes, by sas.

Explanation:

Step1: Identify given information

We have right - angled triangles $\triangle ABC$ and $\triangle DEF$ with one pair of legs equal (the single - ticked sides) and the right angles equal ($\angle B=\angle E = 90^{\circ}$) and the other pair of legs equal (the double - ticked sides).

Step2: Recall congruence criteria

The Side - Angle - Side (SAS) congruence criterion states that if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, then the two triangles are congruent. Here, in $\triangle ABC$ and $\triangle DEF$, $AB = DE$, $\angle B=\angle E$, and $BC = EF$.

Answer:

d. Yes, by SAS.