Triangle Congruence Proofs

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What is Triangle Congruence?

Back

Triangle Congruence refers to the condition where two triangles are considered congruent if their corresponding sides and angles are equal.

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What does SAS stand for in triangle congruence?

Back

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

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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 CPCTC?

Back

CPCTC stands for Corresponding Parts of Congruent Triangles are Congruent, a principle used to prove that corresponding angles and sides of congruent triangles are equal.

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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 Angle Bisector?

Back

An angle bisector is a line or ray that divides an angle into two equal parts.

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What is the definition of Congruence in geometry?

Back

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

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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 lengths.

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What is the Alternate Interior Angles Theorem?

Back

The Alternate Interior Angles Theorem states that if two parallel lines are cut by a transversal, then each pair of alternate interior angles is congruent.

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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.