Triangle Congruence

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What does HL stand for in triangle congruence?

Back

HL stands for Hypotenuse-Leg, a theorem used to prove the congruence of right triangles.

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What is the SAS postulate?

Back

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

Front

What is the ASA postulate?

Back

ASA 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 is the AAS postulate?

Back

AAS 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 does SSS stand for in triangle congruence?

Back

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

Front

How can you determine if two triangles are congruent using HL?

Back

To determine if two triangles are congruent using HL, check if both triangles are right triangles and if the lengths of the hypotenuse and one leg are equal.

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What is the significance of congruent triangles in geometry?

Back

Congruent triangles have the same size and shape, which means their corresponding sides and angles are equal, allowing for various geometric proofs and applications.

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Can two triangles be congruent if only one side is equal?

Back

No, two triangles cannot be congruent if only one side is equal; at least two sides and the included angle or specific postulates must be satisfied.

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What is the difference between congruence and similarity in triangles?

Back

Congruence means the triangles are identical in size and shape, while similarity means they have the same shape but may differ in size.

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What is the purpose of triangle congruence theorems?

Back

Triangle congruence theorems are used to prove that two triangles are congruent, which is essential for solving problems in geometry.