Question

Based only on the information given in the diagram, which congruence theorems or postulates could be given as reasons why DEF ≅ KLM? Check all that apply.

A. LL
B. SAS
C. HA
D. LA
E. AAS
F. HL

Answer 1

The postulates that prove ∆EDF congruent to ∆LKM are (Side-angle-side,SAS) and (Hypotenuse -Leg,HL).

Conditions for congruence of triangles.

Triangles are congruent if corresponding sides are equal, corresponding angles are equal, or a side-angle-side (SAS), angle-side-angle (ASA), or side-side-side (SSS), Hypotenuse -Leg(HL) condition is satisfied

From the figure

ED ≅ LK(Given)

DF ≅ KM(Given)

∠EDF ≅∠LKM (Given)

EF ≅ LM (hypotenuse)

Therefore,

∆EDF ≅ ∆LKM (Side-angle-side)

Since

m∠D = m∠K = 90⁰

EF ≅ LM (hypotenuse)

∆EDF ≅ ∆LKM (Hypotenuse -Leg)

The postulates that prove ∆EDF congruent to ∆LKM are (Side-angle-side,SAS) and (Hypotenuse -Leg,HL).