Question

Complete each congruency statement, and name the rule used.

If you cannot show the triangles are congruent from the given information, leave the triangle's name blank and write CNBD for "CanNot Be Determined" in place of the rule.

Help if you can! Thx :)

Answer 1

ΔGAS ≅ ΔIOL by AAS

Explanation:

From the dashes on the angles and sides of the given triangles:

• ∠G ≅ ∠I
• ∠A ≅ ∠O
• AS ≅ OL

Therefore, the two triangles have two corresponding congruent angles and a congruent corresponding non-included side. This means we can show that the triangles are congruent by the AAS congruence Theorem.

Angle-Angle-Side (AAS) Congruence Theorem

If any two angles and the non-included side of one triangle are congruent to the corresponding parts of another triangle, the triangles are congruent.

Therefore:

• ΔGAS ≅ ΔIOL by AAS

Answer 2

ΔGAS ≅ ΔIOLby AAS

Explanation:

We can prove congruence by the AAS Theorem

AAS Theorem

By definition, AAS congruence rule states that if any two angles and the non-included side of one triangle are equal to the corresponding angles and the non-included side of the other triangle, the two triangles must be congruent

In triangles ΔGAS and ΔIOL

We have:
∠G ≅ ∠I
m∠A ≅ m∠O

AS ≅ OL

AS is the non-included side of ΔGAS and OL is the non-included side of ΔIOL

Therefore we have two corresponding angles congruent and the non-included side of each of these triangles also congruent

Therefore by the AAS (Angle-Angle-Side) theorem, the two triangles are congruent

ΔGAS ≅ ΔIOL by AAS