Congruent Triangles

Front

What are congruent triangles?

Back

Triangles that have the same size and shape, meaning their corresponding sides and angles are equal.

Front

What does the ASA postulate stand for?

Back

Angle-Side-Angle postulate: If two angles and the included side of one triangle are equal to two angles and the included side of another triangle, then the triangles are congruent.

Front

What does the SAS postulate stand for?

Back

Side-Angle-Side postulate: 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.

Front

What does the SSS postulate stand for?

Back

Side-Side-Side postulate: If all three sides of one triangle are equal to all three sides of another triangle, then the triangles are congruent.

Front

What does the AAS postulate stand for?

Back

Angle-Angle-Side postulate: 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

Can triangles be congruent if they have the same angles but different side lengths?

Back

No, triangles with the same angles must also have the same side lengths to be congruent.

Front

What is the significance of congruent triangles in geometry?

Back

Congruent triangles are used to prove other geometric properties and theorems, as well as in real-world applications like engineering and architecture.

Front

If two triangles have two sides of equal length and the angle between them is equal, what postulate can be used to prove they are congruent?

Back

SAS postulate.

Front

If two triangles have three sides of equal length, what postulate can be used to prove they are congruent?

Back

SSS postulate.

Front

If two triangles have two angles equal and a non-included side equal, what postulate can be used to prove they are congruent?

Back

AAS postulate.