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