triangle congruence

Front

What does AAS stand for in triangle congruence?

Back

AAS stands for Angle-Angle-Side, a rule 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 rule 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 rule 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 rule 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.

Front

What does HL stand for in triangle congruence?

Back

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

Front

Are triangles with two sides and a non-included angle congruent?

Back

No, this is known as the SSA condition, which does not guarantee triangle congruence.

Front

If two triangles have two angles congruent, what can be said about the third angle?

Back

The third angle must also be congruent due to the Triangle Sum Theorem, which states that the sum of the angles in a triangle is always 180 degrees.

Front

What is the Triangle Sum Theorem?

Back

The Triangle Sum Theorem states that the sum of the interior angles of a triangle is always 180 degrees.

Front

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

Back

No, at least two sides and the included angle or two angles and the included side must be known to establish congruence.

Front

What is the difference between congruent triangles and similar triangles?

Back

Congruent triangles have the same size and shape (all corresponding sides and angles are equal), while similar triangles have the same shape but not necessarily the same size (corresponding angles are equal, but corresponding sides are in proportion).