Triangle Congruency

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What is Triangle Congruency?

Back

Triangle congruency refers to the condition where two triangles are considered congruent if they have the same size and shape, meaning their corresponding sides and angles are equal.

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What does the SSS postulate state?

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The SSS (Side-Side-Side) postulate 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 does the SAS postulate state?

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The SAS (Side-Angle-Side) postulate 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 two triangles are congruent.

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What does the ASA postulate state?

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The ASA (Angle-Side-Angle) postulate 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 two triangles are congruent.

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What does the AAS postulate state?

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The AAS (Angle-Angle-Side) postulate 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 two triangles are congruent.

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What is the HL theorem?

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The HL (Hypotenuse-Leg) theorem states that if the hypotenuse and one leg of a right triangle are equal to the hypotenuse and one leg of another right triangle, then the two triangles are congruent.

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What is the significance of congruency statements?

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Congruency statements indicate that two triangles are congruent and provide a way to compare corresponding parts (sides and angles) of the triangles.

Front

If ∆ABC≅∆XYZ, what can we conclude about the sides AB and XY?

Back

AB≅XY, meaning side AB of triangle ABC is congruent to side XY of triangle XYZ.

Front

What is the definition of corresponding angles in congruent triangles?

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Corresponding angles are angles that are in the same relative position in two different triangles that are congruent.

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What is the definition of corresponding sides in congruent triangles?

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Corresponding sides are sides that are in the same relative position in two different triangles that are congruent.