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SAS (Side-Angle-Side) Postulate

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SAS (Side-Angle-Side) Postulate

Study Guide

Key Definition

The SAS (Side-Angle-Side) 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: $\triangle ABC \cong \triangle DEF$ if $AB \cong DE$, $BC \cong EF$, and $\angle B \cong \angle E$.

Important Notes

Congruent triangles have corresponding sides and angles that are equal.
The order of vertices in triangle notation must match when declaring congruence.
Use the SAS Postulate to prove congruence without measuring all angles and sides.
Congruence is denoted by $\cong$.
The included angle is the angle between the two sides being compared.

Mathematical Notation

$\triangle$ represents a triangle

$\angle$ indicates an angle

$\cong$ denotes congruence

$\overline{AB}$ is a line segment between points A and B

$\angle ABC$ is the angle at point B between lines AB and BC

Remember to use proper notation when solving problems

Why It Works

The SAS Postulate works because if two sides and the included angle are identical in two triangles, the remaining side and angles must also be equal, ensuring the triangles are congruent.

Remember

To apply the SAS Postulate, ensure you have two sides and the included angle. Use $\cong$ to denote congruence.

Quick Reference

SAS Postulate:$If AB \cong DE$, $BC \cong EF$, $\angle B \cong \angle E$, then $\triangle ABC \cong \triangle DEF$

Understanding SAS (Side-Angle-Side) Postulate

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Video explanation of this concept

Beginner

Start here! Easy to understand

Beginner Explanation

The SAS Postulate states that $\triangle ABC \cong \triangle DEF$ if two sides and the included angle of one triangle are congruent to two sides and the included angle of another.

Practice Problems

Test your understanding with practice problems

Quick Quiz

Single Choice Quiz

Beginner

If $\overline{AB} \cong \overline{DE}$, $\overline{BC} \cong \overline{EF}$, and $\angle B \cong \angle E$, which statement is true?

Real-World Problem

Question Exercise

Intermediate

Kite Proof

A kite is formed by triangles ABC and ADC. In this kite, AB = AD = 5 cm, BC = DC = 7 cm, and ∠B = ∠D = 60°. Prove that $\triangle ABC$ is congruent to $\triangle ADC$ using the SAS Postulate.

Thinking Challenge

Thinking Exercise

Intermediate

Think About This

Given triangles XYZ and MNP such that $\overline{XY} \cong \overline{MN}$, $\overline{YZ} \cong \overline{NP}$, and $\angle Y \cong \angle N$, but $\overline{XZ}$ is not congruent to $\overline{MP}$, can you determine if $\triangle XYZ$ is congruent to $\triangle MNP$?

Challenge Quiz

Single Choice Quiz

Advanced

Which of the following sets of triangles can be proven congruent using the SAS Postulate?

Recap

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Review key concepts and takeaways