Proving Triangles Congruent

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What does AAS stand for in triangle congruence?

Back

AAS stands for Angle-Angle-Side, a criterion for triangle congruence where two angles and a non-included side of one triangle are congruent to two angles and the corresponding non-included side of another triangle.

Front

What does ASA stand for in triangle congruence?

Back

ASA stands for Angle-Side-Angle, a criterion for triangle congruence where two angles and the included side of one triangle are congruent to two angles and the corresponding included side of another triangle.

Front

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 congruent to two sides and the corresponding included angle of another triangle.

Front

What does SSS stand for in triangle congruence?

Back

SSS stands for Side-Side-Side, a criterion for triangle congruence where all three sides of one triangle are congruent to all three sides of another triangle.

Front

What is the Reflexive Property in geometry?

Back

The Reflexive Property states that any geometric figure is congruent to itself. For example, if triangle ABC is being compared to triangle ABC, they are congruent by the Reflexive Property.

Front

What are Vertical Angles?

Back

Vertical angles are the angles opposite each other when two lines intersect. They are always congruent.

Front

How can you prove triangles are congruent using Vertical Angles?

Back

If two triangles share a pair of vertical angles, and you have another pair of congruent angles or sides, you can use the ASA or AAS criteria to prove the triangles are congruent.

Front

What is the significance of the included angle in triangle congruence?

Back

The included angle is the angle formed between two sides of a triangle. It is crucial in the SAS and ASA criteria for proving triangle congruence.

Front

Can two triangles be congruent if only one side is known?

Back

No, you need at least two sides and the included angle (SAS) or two angles and a non-included side (AAS) to prove congruence.

Front

What is the difference between AAS and ASA?

Back

AAS involves two angles and a non-included side, while ASA involves two angles and the included side.