Triangle Congruence Theorems & Proofs

Front

What is the Reflexive Property?

Back

The Reflexive Property states that any geometric figure is congruent to itself. For example, triangle ABC is congruent to triangle ABC.

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Which triangle congruence theorem is used when two sides and the included angle are known?

Back

SAS (Side-Angle-Side) 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 does HL stand for in triangle congruence?

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HL stands for Hypotenuse-Leg theorem, which 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 is CPCTC?

Back

CPCTC stands for 'Corresponding Parts of Congruent Triangles are Congruent.' It is used to prove that corresponding angles and sides of congruent triangles are equal.

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What is the Vertical Angle Theorem?

Back

The Vertical Angle Theorem states that vertical angles are congruent. If two angles are opposite each other when two lines intersect, they are equal in measure.

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What is the SSS theorem?

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SSS (Side-Side-Side) 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 AAS theorem?

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AAS (Angle-Angle-Side) 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 SSA condition?

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SSA (Side-Side-Angle) condition does not guarantee triangle congruence. It is possible to have two different triangles with the same two sides and a non-included angle.

Front

What is the definition of congruence in geometry?

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In geometry, congruence 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 purpose of a proof in geometry?

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