Question

Can the triangles be proven congruent with the information given in the diagram? If so, state the theorem you would use.noyes; ASA Congruence Theoremyes; AAS Congruence Theorem

Answer 1

The diagramof the triangles is shown below

Looking at the two traingles, they meet at a vertex. Vertically opposite angles are equal.

Answer 2

Yes. The triangles can be proven congruent by AAS congruence theorem

What is AAS congruence theorem

The AAS Congruence Theorem states that if two angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of another triangle, then the two triangles are congruent.

In this case, one pair of angle is given to be congruent. The second pair of congruent triangles is found by vertical angle theorem.

The corresponding positions of the congruent sides (non-included side) and the angles makes it possible to use the AAS congruence theorem