Triangle Congruence Proofs

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What does SSS stand for in triangle congruence?

Back

SSS stands for Side-Side-Side, a criterion for triangle congruence stating that if three sides of one triangle are equal to three sides of another triangle, the triangles are congruent.

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What does SAS stand for in triangle congruence?

Back

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

Front

What does ASA stand for in triangle congruence?

Back

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

Front

What does AAS stand for in triangle congruence?

Back

AAS stands for Angle-Angle-Side, a criterion for triangle congruence stating 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, the triangles are congruent.

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What is the Reflexive Property?

Back

The Reflexive Property states that any geometric figure is congruent to itself, meaning that for any triangle ∆ABC, ∆ABC ≅ ∆ABC.

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What is the Vertical Angles Theorem?

Back

The Vertical Angles Theorem states that when two lines intersect, the opposite (or vertical) angles are congruent.

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What is the Definition of Congruence?

Back

Congruence in geometry means that two figures have the same shape and size, and can be made to coincide by rigid motions (translations, rotations, reflections).

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What is the Definition of Midpoint?

Back

The midpoint of a line segment is the point that divides the segment into two equal parts.

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What is the significance of Given in a proof?

Back

'Given' refers to the information that is provided in a problem or proof, which serves as the starting point for reasoning.

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What is the purpose of a proof in geometry?

Back

A proof in geometry is a logical argument that establishes the truth of a statement or theorem based on previously established statements, definitions, and axioms.