Triangle Congruence

Front

What does AAS stand for in triangle congruence?

Back

AAS stands for Angle-Angle-Side, a postulate that states 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.

Front

What is the ASA postulate?

Back

ASA stands for Angle-Side-Angle, a postulate that states if two angles and the included side of one triangle are equal 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 postulate that states if all three sides of one triangle are equal to all three sides of another triangle, then the triangles are congruent.

Front

What is the SAS postulate?

Back

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

Front

What is the SSA condition in triangle congruence?

Back

SSA stands for Side-Side-Angle, which is not a valid postulate for proving triangle congruence because it can lead to ambiguous cases.

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.

Front

Can two triangles be congruent if only one angle and two sides are known?

Back

Not necessarily; this is known as the SSA condition, which does not guarantee congruence.

Front

What is the importance of congruence in triangles?

Back

Congruence in triangles allows us to conclude that the triangles have the same shape and size, which is essential in various applications in geometry.

Front

How can you prove triangles are congruent using SSS?

Back

To prove triangles are congruent using SSS, show that all three corresponding sides of the triangles are equal.

Front

What is the significance of the included angle in SAS?

Back

In SAS, the included angle is crucial because it is the angle formed between the two sides being compared, ensuring the triangles are congruent.