Triangle Congruence Theorems

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What are the Triangle Congruence Theorems?

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The Triangle Congruence Theorems include Side-Side-Side (SSS), Side-Angle-Side (SAS), Angle-Side-Angle (ASA), Angle-Angle-Side (AAS), and Hypotenuse-Leg (HL) for right triangles.

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What does it mean for two triangles to be congruent?

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Two triangles are congruent if they have the same size and shape, meaning their corresponding sides and angles are equal.

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What is the Reflexive Property of Equality (POE)?

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The Reflexive Property states that any geometric figure is congruent to itself.

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What is the Side-Side-Side (SSS) Congruence Theorem?

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The SSS Congruence Theorem states that if three sides of one triangle are equal to three sides of another triangle, then the triangles are congruent.

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What is the Side-Angle-Side (SAS) Congruence Theorem?

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The SAS Congruence Theorem 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.

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What is the Angle-Side-Angle (ASA) Congruence Theorem?

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The ASA Congruence Theorem 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.

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What is the Angle-Angle-Side (AAS) Congruence Theorem?

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The AAS Congruence Theorem 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.

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What is the Hypotenuse-Leg (HL) Congruence Theorem?

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The HL Congruence 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 triangles are congruent.

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What are vertical angles?

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Vertical angles are the angles opposite each other when two lines intersect. They are always congruent.

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How can you determine if two triangles are congruent using the information given?

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You can determine if two triangles are congruent by using the congruence theorems (SSS, SAS, ASA, AAS, HL) based on the information about their sides and angles.