Triangle Congruence

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What does SAS stand for in triangle congruence?

Back

SAS stands for Side-Angle-Side, a theorem that states if two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle, then the two triangles are congruent.

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What is the SSS Postulate?

Back

The SSS Postulate stands for Side-Side-Side, which states that if three sides of one triangle are equal to three sides of another triangle, then the two triangles are congruent.

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What is the AAS Theorem?

Back

The AAS Theorem stands for Angle-Angle-Side, which states that if two angles and a non-included side of one triangle are equal to two angles and the corresponding non-included side of another triangle, then the triangles are congruent.

Front

What is the ASA Postulate?

Back

The ASA Postulate stands for Angle-Side-Angle, which states that if two angles and the included side of one triangle are equal to two angles and the included side of another triangle, then the triangles are congruent.

Front

What does SSA stand for in triangle congruence?

Back

SSA stands for Side-Side-Angle, which does not guarantee triangle congruence. It can lead to ambiguous cases where two different triangles can be formed.

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Back

The corresponding sides and angles of congruent triangles are equal.

Front

How can you prove triangles are congruent using the SAS Postulate?

Back

To prove triangles are congruent using the SAS Postulate, show that two sides and the included angle of one triangle are equal to two sides and the included angle of another triangle.

Front

What is the significance of congruence in triangles?

Back

Congruence in triangles indicates that the triangles have the same shape and size, allowing for the transfer of properties and measurements between them.

Front

What is the relationship between the angles and sides in congruent triangles?

Back

In congruent triangles, corresponding angles are equal, and corresponding sides are proportional.

Front

Can two triangles be congruent if only one angle and two non-included sides are known?

Back

No, this is known as the SSA condition, which does not guarantee congruence due to the possibility of forming two different triangles.