Question

question 6 of 10
based only on the information given in the diagram, which congruence theorems or postulates could be given as reasons why \\( \triangle hij \cong \triangle klm \\)?
check all that apply.
a. asa
b. la
c. hl
d. aas
e. ll
f. ha

Explanation:

• LA (Leg - Angle): For right - angled triangles, if a leg and an acute angle of one right - triangle are congruent to a leg and an acute angle of another right - triangle, the triangles are congruent. Here, we have right - angled triangles (\(\angle H=\angle K = 90^{\circ}\)), a pair of legs (the marked sides) and a pair of acute angles (\(\angle J=\angle M\)) that can satisfy the LA criterion.
• AAS (Angle - Angle - Side): 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. We have two angles (\(\angle H=\angle K = 90^{\circ}\) and \(\angle J=\angle M\)) and a non - included side (the marked sides) that can satisfy the AAS criterion.

Answer:

B. LA, D. AAS