Question

Which congruence theorems can be used to prove ΔEFG ≅ ΔJHG? Select two options.

Triangles E F G and J H G are connected at point G. Sides F G and and G H are congruent. Sides E F and H J are parallel.

HL
SAS
SSS
ASA
AAS

Answer 1

Answer:

ASA  and AAS

Step-by-step explanation:

We do not know if these are right triangles; therefore we cannot use HL to prove congruence.

We do not have 2 or 3 sides marked congruent; therefore we cannot use SSS or SAS to prove congruence.

We are given that EF is parallel to HJ.  This makes EJ a transversal.  This also means that ∠HJG and ∠GEF are alternate interior angles and are therefore congruent.  We also know that ∠EGF and ∠HGJ are vertical angles and are congruent.  This gives us two angles and a non-included side, which is the AAS congruence theorem.

Since EF and HJ are parallel and EJ is a transversal, ∠JHG and ∠EFG are alternate interior angles and are congruent.  Again we have that ∠EGF and ∠HGJ are vertical angles and are congruent; this gives us two angles and an included side, which is the ASA congruence theorem.

Answer 2

The congruence theorems that can be used to prove ΔEFG ≅ ΔJHG are; ASA and AAS

It is impossible to know if these are right triangles from the information given;

On this note, only one side of each triangle is marked congruent;

Hence, we are unable use SSS or SAS to affirm congruence.

• Additionally, since EF is parallel to HJ. Therefore, line EJ is a transversal. This also means that ∠HJG and ∠GEF are alternate (z-angles) interior angles and are therefore congruent.

• Similarly, ∠EGF and ∠HGJ are vertical angles and are congruent. We have therefore established the AAS congruence theorem.

• Since EF and HJ are parallel and EJ is a transversal, ∠JHG and ∠EFG are alternate (z-angles) interior angles and are congruent.

• Similarly, ∠EGF and ∠HGJ are vertical angles and are congruent; This gives us two angles and an included side, which is the ASA congruence theorem.

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