Geometry Chapter 5 - Congruent Triangles

Angle-Side-Angle Congruence Postulate (ASA)

if two angles and the included side are congruent to two angles and the included side of another triangle then the two triangles are congruent

Side-Angle-Side Congruence Postulate (SAS)

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

theorems to remember

definition of perpendicular lines right angles theorem corresponding angles theorem definition of mdpt vertical angle theorem alt int angle theorem reflexive prop of cong

Perpendicular Bisector Theorem

if a point is on the perpendicular bisector of a segment then it is equidistant from the endpoints of the segment

Perpendicular Bisector

A line that is perpendicular to a segment at its midpoint.

Angle Bisector Theorem

If a point is on the bisector of an angle, then it is equidistant from the two sides of the angle

Hypotenuse-Leg Congruence Theorem: HL

If the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and a leg of another right triangle, then the triangles are congruent

Side-Side-Side Congruence Postulate (SSS)

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

Angle-Angle-Side Congruence Theorem (AAS)

If two angles and a nonincluded side of one triangle are congruent to the corresponding angles and noncluded side of another triangle, then the triangles are congruent.