Geometry Unit 5.4

Reflexive Property

A quantity is congruent (equal) to itself. a = a

corresponding angles theorem

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

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.

perpendicular lines

Lines that intersect to form right angles

CPCTC (Corresponding Parts of Congruent Triangles are Congruent)

means they're in the same position in the 2 triangles.

Hypotnuse

the side opposite of a right triangle in a right trangle

Definition of Vertical Angles

two angles whose sides form two pairs of opposite rays

defintion of congruence

equal in measure

AAS

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

Midpoint

A point that divides a segment into two congruent segments

perpendicular bisector

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

Definition of a Right Angle

An angle is a right angle if and only if it equals 90 degrees

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 Bisector Theorem

If a ray bisects an angle in a triangle, then it cuts the opposite side proportionally to the other two sides

Substitution Property

If a=b, then a can be substituted for b in any equation or expression

SSS

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

ASA

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.

Alternate Interior Angles Theorem

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

Orthocenter

The point of concurrency of the altitudes of a triangle

centroid

The point of concurrency of the medians of a triangle

concurrent lines

Three or more lines that intersect at a common point

Vertical Angles Theorem

Vertical angles are congruent

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

median of a triangle

a segment from a vertex to the midpoint of the opposite side