Note: Your teacher will grade your responses to questions 7–10 to ensure you receive proper credit for your answers.

Question

State whether triangleABC and triangleAED are congruent. Justify your answer.

Triangles ABC and AEC are labeled on a diagram.

Answer 1

In order to determine if triangle ABC and triangle AED are congruent, we need to compare their corresponding sides and angles.

From the information given, we know that triangles ABC and AEC share two corresponding angles, angle A and angle C. This is because these angles are formed by the intersection of the same two lines, AC and EC.

Additionally, we know that the lengths of corresponding sides in triangles ABC and AEC are equal. This is because segment AC is a shared side between the two triangles.

Therefore, by the angle-side-angle (ASA) congruence criterion, we can conclude that triangle ABC and triangle AED are congruent.