Question

question 1 of 10
based only on the information given in the diagram, which congruence theorems or postulates could be given as reasons why △def≅△jkl?
check all that apply.
a. la
b. aas
c. hl
d. asa
e. ll
f. sas

Explanation:

Step1: Identify right - angled triangles

Both \(\triangle DEF\) and \(\triangle JKL\) are right - angled triangles as indicated by the right - angle symbols.

Step2: Analyze congruence conditions

We see that one leg of each triangle is congruent (the marked sides) and one non - right angle of each triangle is congruent.

Step3: Recall congruence postulates

The LA (Leg - Angle) postulate states that if a leg and an acute angle of one right - triangle are congruent to the corresponding leg and acute angle of another right - triangle, the two right - triangles are congruent. Here we have a leg and an acute angle congruent, so LA applies. Also, the AAS (Angle - Angle - Side) postulate can be used as we have two angles (the right - angle and the marked non - right angle) and a non - included side (the marked leg) congruent.

Answer:

A. LA
B. AAS