Proving Triangle Congruence with SAS (Side-Angle-Side) Postulate in Geometry

SAS

SAS (Short for “Side-Angle-Side”) is a postulate used in geometry to prove two triangles are congruent

SAS (Short for “Side-Angle-Side”) is a postulate used in geometry to prove two triangles are congruent. The SAS postulate states that if two sides and the included angle of one triangle are congruent to the corresponding two sides and included angle of another triangle, then the two triangles are congruent.

To use the SAS postulate to prove triangle congruence, you need to show that the two sides and the included angle are congruent. Here’s an example to illustrate how to use the SAS postulate:

1. Given: Triangle ABC and triangle DEF, with AB ≅ DE, BC ≅ EF, and ∠BAC ≅ ∠EDF.
2. To prove: Triangle ABC ≅ Triangle DEF using the SAS postulate.

Proof:
Step 1: Given information: AB ≅ DE, BC ≅ EF, and ∠BAC ≅ ∠EDF.
Step 2: Side AB ≅ side DE (Given).
Step 3: Side BC ≅ side EF (Given).
Step 4: ∠BAC ≅ ∠EDF (Given).
Step 5: By the SAS postulate, triangle ABC ≅ triangle DEF.

By using the SAS postulate, we have shown that if two sides and the included angle of one triangle are congruent to the corresponding two sides and included angle of another triangle, then the two triangles are congruent.

Remember to clearly state the given information, the statements made in the proof, and the reason for each statement. This will help ensure a clear and logical explanation of triangle congruence using the SAS postulate.

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