Question

Tell which postulate or theorem you would use to show that the triangles are congruent. Explain your reasoning.

Answer 1

The postulate or theorem used to show that triangles are congruent depends on the given information about the triangles. Commonly used postulates and theorems include SSS, SAS, ASA, and AAS.

Step-by-step explanation:

The postulate or theorem that we would use to show that the triangles are congruent depends on the given information about the triangles. Here are some commonly used postulates and theorems:

• The Side-Side-Side (SSS) Congruence Postulate: If all three sides of one triangle are congruent to the corresponding sides of another triangle, then the triangles are congruent.
• The Side-Angle-Side (SAS) Congruence Theorem: 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.
• The Angle-Side-Angle (ASA) Congruence Theorem: If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent.
• The Angle-Angle-Side (AAS) Congruence Theorem: 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 triangles are congruent.

To determine which postulate or theorem to use, we must compare the given information about the triangles with the conditions stated in each postulate or theorem.