Question

Given: , ∠DAC ≅ ∠BCA Prove: ∆ADC ≅ ∆CBA Look at the proof. Name the postulate you would use to prove the two triangles are congruent. SAS Postulate SSS Postulate AAA Postulate

Answer 1

The image suggests a proof demonstrating the congruence of two triangles,
`\( \triangle ADC \)` and
`\( \triangle CBA \)`, with the given information:

-
`\( AD \cong CB \)` (sides)

-
`\( \angle DAC \cong \angle BCA \)` (angles)

-
`\( AC \cong AC \)` (sides)

The congruence postulate that applies to this situation is the Side-Angle-Side (SAS) Postulate. The SAS Postulate states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent.

In this proof, side
`\( AC \)` is the included side between angle
`\( \angle DAC \)` and side
`\( AD \)` in triangle
`\( \triangle ADC \)`, and between angle
`\( \angle BCA \)` and side
`\( CB \)` in triangle
`\( \triangle CBA \)`. This satisfies the conditions of the SAS Postulate. Therefore, we can conclude that
`\( \triangle ADC \cong \triangle CBA \)` by the SAS Postulate.

Answer 2

SAS Postulate

Explanation:

The contributors to the proof are listed in the left column. They consist of a congruent Side, a congruent Angle, and a congruent Side. The SAS Postulate is an appropriate choice.