Triangle Congruence Theorems

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What does AAS stand for in triangle congruence?

Back

AAS stands for Angle-Angle-Side, a theorem that states if two angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of another triangle, then the triangles are congruent.

Front

What does ASA stand for in triangle congruence?

Back

ASA stands for Angle-Side-Angle, a theorem that states if two angles and the included side of one triangle are congruent to two angles and the corresponding included side of another triangle, then the triangles are congruent.

Front

What does SSS stand for in triangle congruence?

Back

SSS stands for Side-Side-Side, a theorem that states if all three sides of one triangle are congruent to all three sides of another triangle, then the triangles are congruent.

Front

What does SAS stand for in triangle congruence?

Back

SAS stands for Side-Angle-Side, a theorem that states if two sides and the included angle of one triangle are congruent to two sides and the corresponding included angle of another triangle, then the triangles are congruent.

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What is the Vertical Angle Theorem?

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The Vertical Angle Theorem states that vertical angles are congruent, meaning that when two lines intersect, the angles opposite each other are equal.

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What is the Reflexive Property?

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

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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 transformations such as translation, rotation, or reflection.

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What is the significance of the HL theorem?

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The HL theorem, or Hypotenuse-Leg theorem, 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 triangles are congruent.

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How can you prove triangles are congruent using AAS?

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To prove triangles are congruent using AAS, show that two angles and a non-included side of one triangle are congruent to the corresponding two angles and non-included side of another triangle.

Front

How can you prove triangles are congruent using ASA?

Back

To prove triangles are congruent using ASA, demonstrate that two angles and the included side of one triangle are congruent to the corresponding two angles and included side of another triangle.