Congruent Triangles

Front

What does SAS stand for in triangle congruence?

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 included angle 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 postulate that states 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 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 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 HL postulate in triangle congruence?

Back

HL stands for Hypotenuse-Leg, a postulate that applies to right triangles, stating that if the hypotenuse and one leg of one right triangle are equal to the hypotenuse and one leg of another right triangle, then the triangles are congruent.

Front

What additional information is needed to prove triangles congruent using ASA?

Back

You need to know the length of the side between the two angles (the included side) or the measure of the third angle.

Front

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

Back

No, two triangles cannot be congruent if only one side is equal; more information about angles or other sides is needed.

Front

If triangle GEF is congruent to triangle GJH by AAS, what does that imply?

Back

It implies that two angles and a non-included side of triangle GEF are equal to two angles and the corresponding non-included side of triangle GJH.

Front

What is the significance of congruent triangles in geometry?

Back

Congruent triangles are significant because they allow us to establish that two shapes are identical in size and shape, which is fundamental in proofs and constructions.

Front

What is the relationship between congruent triangles and parallel lines?

Back

Congruent triangles can be formed by intersecting parallel lines with transversals, leading to equal angles and proportional sides.