Triangle Congruence Theorems

Front

What is AAS Congruence?

Back

AAS Congruence states that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.

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What is the SSS Congruence Theorem?

Back

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

Front

What does SAS Congruence stand for?

Back

SAS Congruence states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent.

Front

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 HL Congruence Theorem?

Back

HL Congruence states that if the hypotenuse and one leg of a right triangle are congruent to the hypotenuse and one leg of another right triangle, then the two triangles are congruent.

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Which triangle congruence theorem cannot be used to prove triangle congruence?

Back

AAA (Angle-Angle-Angle) cannot be used to prove triangle congruence because it only shows that the triangles are similar, not necessarily congruent.

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What is the Vertical Angles Theorem?

Back

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

Front

What is the definition of midpoint?

Back

A midpoint is a point that divides a line segment into two equal parts.

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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 the pairs of alternate interior angles are congruent.

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What is the significance of the Definition of Equality in geometry?

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The Definition of Equality states that if two quantities are equal, then they can be substituted for one another in any equation or expression.