Chapter 5 Triangle Congruence

Definition of Midpoint

The midpoint of a segment is the point that divides the segment into two congruent segments.

Reflexive Property of Segment Congruence

When a side is equal to itself.

Definition of Segment Bisector

A segment bisector is a point, ray, line, line segment, or plane that intersects the segment at its midpoint. A midpoint or a segment bisector bisects a segment.

Vertical Angles Theorem

When 2 lines intersect, the angles formed opposite of each other are congruent.

Reflexive Property of Angle Congruence

When an angle is equal to itself.

Definition of Angle Bisector

An angle bisector is a ray that divides an angle into two angles that are congruent.

Third Angles Theorem

If two angles of one triangle are congruent to two angles of another triangle, then the third angles are also congruent.

Corresponding Angles Theorem

If two parallel lines are cut by a transversal, then the pairs of corresponding angles are congruent.

Alternate Interior Angles Theorem

If two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent.

Base Angles Theorem

If two sides of a triangle are congruent, then the angles opposite them are congruent.

Definition of Perpendicular Lines

Two lines that intersect to form a right angle.

Right Angles congruence Theorem

All right angles are congruent.

SSS

(Side - Side - Side)

Three pairs of congruent sides.

SAS

(Side - Angle - Side)

Two pairs of congruent sides and an included angle.

ASA

(Angle - Side - Angle)

Two pairs of congruent angles and an included side.

AAS

(Angle - Angle - Side)

Two pairs of congruent angles and a non included side

HL

(Hypotenuse - Leg)

RIGHT TRIANGLES ONLY -- The hypotenuse and any one leg of a right triangle.