Triangle Congruence Postulates/Theorem

Side Side Side (SSS) Postulate

If three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent.

Angle Side Angle (ASA) Postulate

If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent.

Angle Angle Side (AAS) Theorem

If two pairs of angles and a pair of non-included sides are congruent, then the triangles are congruent

Side Angle Side (SAS) Postulate

If two sides and the included angle of one triangle are congruent to two sides and the included angle of a second triangle, then the two triangles are congruent.

Side Side Angle (SsA) Theorem

If two sides of a triangle and the angle opposite the larger side are congruent to corresponding parts in another triangle, then the two are equal

Requirement for HLR 2)

The triangles have congruent hypotenuses

Requirement for HLR 1)

There are two right triangles

Requirement for HLR 3)

There is one pair of congruent legs

CPCTC

corresponding parts of congruent triangles are congruent

Isosceles Triangle Theorem: If a triangle is an isosceles

then the base angles are congruent

Hypotenuse-Leg-Right-Triangle Theorem: If the hypotenuse and a leg of one right triangle are congruent to the corresponding parts of another right triangle

then the triangles are congruent.

A line and a plane are congruent if and only if

they intersect and the line is perpendicular to all lines in the plane that pass through the point of intersection