Question

Based on only the information given in the diagram, which congruence postulates or theorems can be given as reasons why triangle HEL is ~ to triangle PME? Check all that apply.

Answer 1

Let's go through the choices.

A. HL, hypotenuse-leg. Yes we have a right triangle with congruent hypotenuse and leg which gives us congruent triangles, CHECK

B. HA, hypotenuse actute. Yes we have a right triangle witha congruent hypotenuse and acute angle, so congruent triangles, CHECK.

C. LL. leg leg. We don't know HL=PE so we can't use this theorem here. NO.

D. SAS, side angle side. For this one we first have to prove angle HEL is congruent to angle PME which is easily done with the Triangle Angle theorem (two congruent angles means three congruent angles) and then we can use SAS because then we have congruent sides and a congruent included angle. This one's a judgement call, I'll say NO because of the two steps.

E. AAS. Angle Angle Side, yes we have two congruent angles and a side. CHECK

F. ASA. Again we need an additional step before we conclude two angles and an included side are congruent. So again a judgement call, we'll go with NO.