Question

objective: swbat apply the angle - angle - side theorem for triangle congruence.
name: _ date: _ period #:
unit 3 lesson 8: angle - angle - side (aas) theorem
exit ticket 5 minutes
given: \\( \angle r=\angle u \\), ru bisects st
prove: \\( \triangle vsr=\triangle vtu \\)

Explanation:

Step1: Use the property of bisector

Since \(RU\) bisects \(ST\), we have \(SV = TV\) (Definition of bisector).

Step2: Use the vertical - angle property

\(\angle RSV=\angle UTV\) (Vertical angles are congruent).

Step3: Apply AAS theorem

We are given \(\angle R=\angle U\), we have \(SV = TV\) from step 1 and \(\angle RSV=\angle UTV\) from step 2. By the Angle - Angle - Side (AAS) congruence theorem, \(\triangle VSR\cong\triangle VTU\) (AAS: 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).

Answer:

\(\triangle VSR\cong\triangle VTU\) by AAS theorem.