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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

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

Answer :

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).

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