Triangle congruence proofs

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What is Triangle Congruence?

Back

Triangle congruence refers to the condition where two triangles are identical in shape and size, meaning their corresponding sides and angles are equal.

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What does ASA stand for in triangle congruence?

Back

ASA stands for Angle-Side-Angle, a criterion for triangle congruence where two angles and the included side of one triangle are equal to two angles and the included side of another triangle.

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What does AAS stand for in triangle congruence?

Back

AAS stands for Angle-Angle-Side, a criterion for triangle congruence where two angles and a non-included side of one triangle are equal to two angles and the corresponding non-included side of another triangle.

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What does SSS stand for in triangle congruence?

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SSS stands for Side-Side-Side, a criterion for triangle congruence where all three sides of one triangle are equal to the three sides of another triangle.

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What does HL stand for in triangle congruence?

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HL stands for Hypotenuse-Leg, a criterion for triangle congruence applicable to right triangles, where the hypotenuse and one leg of one triangle are equal to the hypotenuse and one leg of another triangle.

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What is the Reflexive Property in triangle congruence?

Back

The Reflexive Property states that a geometric figure is congruent to itself, which is often used to show that a side or angle is shared between two triangles.

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Front

What is the significance of vertical angles in triangle congruence?

Back

Vertical angles are always congruent, which can be used as a reason to establish congruence between triangles that share a vertex.

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How can you determine if two triangles are congruent using the SSA condition?

Back

The SSA condition (Side-Side-Angle) does not guarantee triangle congruence, as it can lead to ambiguous cases where two different triangles can be formed.

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What is the relationship between congruent triangles and their areas?

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Congruent triangles have equal areas because they are identical in shape and size.