Question

Based only on the information given in the diagram, which congruencetheorems or postulates could be given as reasons why ADEF=AKLM?Check all that apply.

Answer 1

Here we are given two right triangles: △DEF and △KLM

Congruent triangles are triangles with equal corresponding sides and equal corresponding angles.

From the figure, we are given two congruent sides and one congruent angle:

DF = KM

∠D = ∠K

ED = LK

Let's check the congruency theorems that apply here:

• SAS(Side Angle Side): The SAS postulate states that if two given sides and the included angle of one triangle are congruent to the two sides and included angle of the other triangle, both triangles are congruent.

Therefore, the SAS postulate applies here.

• LL (leg leg): The LL theorem states that if the legs of one triangle is are congruent to the legs of another triangle, both triangles are congruent.

Therefore, the LL theorem applies here.

Options E and F are correct.

ANSWER:

E. LL

F. SAS