Question

Prove the Angle-Angle-Side Triangle Congruence Condition.

Answer 1

The Angle-Angle-Side (AAS) Triangle Congruence Condition states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.

Step-by-step explanation:

The Angle-Angle-Side (AAS) Triangle Congruence Condition states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.

1. Start with two triangles, Triangle ABC and Triangle DEF, where angle A is congruent to angle D, angle B is congruent to angle E, and side BC is congruent to side EF.
2. Prove that angle C is congruent to angle F. This can be done using the Triangle Angle Sum Theorem, which states that the sum of the angles in a triangle is always 180 degrees.
3. Since angle C is congruent to angle F, all three angles of Triangle ABC are congruent to the corresponding angles of Triangle DEF. Therefore, Triangle ABC and Triangle DEF are congruent by the Angle-Angle (AA) Congruence Condition.