Question

question 5 of 10
based only on the information given in the diagram, which congruence theorems or postulates could be given as reasons why \\( \triangle lmn\cong \triangle opq\\)?
check all that apply.
a. la
b. sas
c. hl
d. aas
e. ll
f. asa

Explanation:

• LA (Leg - Angle): For right - angled triangles, 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 triangles are congruent. Here, we have right - angled triangles ($\angle N=\angle Q = 90^{\circ}$), a pair of congruent legs (marked in the diagram) and a pair of congruent acute angles ($\angle L=\angle O$).
• 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 $\angle N=\angle Q$, $\angle L=\angle O$ (two angles) and a pair of congruent non - included sides (the marked legs).

Answer:

A. LA, D. AAS