Triangle Congruence Postulates: SSS, SAS, ASA, AAS, HL, CPCTC

perpendicular lines

2 lines that intersect to form right angles

Side-Side-Side (SSS)

3 sides of one triangle are congruent to 3 sides of a second triangle, then the 2 triangles are congruent

Reflexive Property

A quantity is congruent (equal) to itself, AB= AB

Perpendicular Bisector Theorem

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

Triangle Angle Bisector Theorem

If a ray bisects an angle of a triangle, then it divides the opposite side into segments proportional to the other two sides

Substitution Property

If a=b then a can be substituted for b

CPCTC (Corresponding Parts of Congruent Triangles are Congruent)

If corresponding parts of a triangle are congruent, then the triangles are congruent

Hypotenuse-Leg (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.

Angle-Angle-Side (AAS)

If two angles and a non- included side of one triangle are congruent to the corresponding angles and non- included side of another triangle, then the triangles are congruent

Angle-Side-Angle (ASA)

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

Side-Angle-Side (SAS)

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

Orthocenter

The point of concurrency of the altitudes of a triangle

Centroid

The point of concurrency of the medians of a triangle

Vertical Angles Theorem

Vertical angles are congruent

Corresponding Angles Theorem

When parallel lines are crossed by a transversal, corresponding angles are congruent

median of a triangle

a line segment drawn from any vertex of the triangle to the midpoint of the opposite side

perpendicular bisector

a line that passes through the midpoint of a side of a triangle, divides the side into congruent parts, and is perpendicular to that side

Def. of Vertical Angles

a pair of opposite congruent angles formed when lines intersect

altitude of a triangle

a perpendicular segment from a vertex to the line containing the opposite side

angle bisector

a ray that divides an angle into two congruent angles

Def. of Right Angle

an angle that measures 90 degrees

def of bisector

divides a segment or an angle into two equal parts

Def. of Congruent

equal in measure

Concurrent Lines

lines in a plane or higher-dimensional space are said to be concurrent if they intersect at a single point

Def. of Midpoint

the point of a segment that divides the segment into 2 congruent segments

Alternate Interior Angles Theorem

when parallel lines are crossed by a transversal, alternate interior angles are congruent