# Teaching Textbook’s Geometry Definitions (with SAT/ACT prep built in!)

Collinear Points are…? Points that lie on the same line
Nonlinear Points are…? Points that do not lie on the same line
A Line Segment is…? A part of a line consisting of two points, called end points, and the set of all points between them
Congruent Line Segments are…? Line segments that have equal lengths
If F, G, and H are collinear and FG + GH = GH then…? G is between F and H
A Ray is…? A part of a line consisting of a given point called the end point and the set of all points on one side of the end point
An Angle is…? The union of two rays having the same end point. The end point is called the vertex of the angle, the rays are called the side of the angle
Congruent Angles are…? Angles that have equal measures
Line PS is between line PQ and line PR. If point S lies in the interior of angle QPR, then…? mAngle QPS + mAngle RPS = mAngle QPR
A Right Angle is…? An angle with a measure of 90?
An Acute Angle is…? An angle with a measure of less than 90?
An Obtuse Angle is…? An angle with a measure of more than 90?, and less than 180?
The Midpoint of a Line Segment is…? The point that divides the line segment into two congruent line segments
A Bisector of Line Segment AB is…? Any line, ray, or line segment which passes through the midpoint of line segment AB
Ray OR is the Bisector of Point R lies in the interior of
Complementary Angles are…? Angles with measures that add to 90?
If two Angles are Complementary to the same Angle or equal Angles then…? They are congruent
Adjacent Angles are…? Angles that have the same vertex share a common side and have no interior points in common
A Linear Pair is…? Two adjacent angles whose exterior sides forms a straight line
If two Angles are a Linear Pair, then…? They are supplementary
Vertical Angles are…? A pair of nonadjacent angles formed by two intersecting lines
Pairs of Vertical Angles are…? Congruent
Perpendicular Angles are…? Lines which intersect to form right angles
Perpendicular Lines intersect to form…? 4 Right Angles
All Right Angles are…? Congruent
A Perpendicular Bisector is…? A line that is perpendicular to across segment and intersects the line segment at its midpoint
Through a given point on a line…? There exists exactly one perpendicular to the given line
Through a given point not on a line…? There exist exactly one perpendicular to the given line
If the exterior sides of a pair of Adjacent Angles are Perpendicular, then…? The angles are complementary
The distance between two points is…? The length of the line segment joining the points
The distance between a line and a point not on the line is…? The length of the perpendicular segment drawn from the point to the line
Parallel lines are…? Lines that lie in the same plane (coplanar) and that never intersect
Line segments, Rays, or Points which lie in the same plane are said to be…? Coplanar
A Transversal is…? A line that intersects two or more lines in different points
When lines are parallel, the alternate interior angles are…? Congruent
When lines are not parallel, the alternate interior angles are…? Not congruent
Proving segments or angles that are congruent…? Show triangles are congruent. Prove segments or angles contained in the triangles are congruent by C.P.C.T.C. (Congruent Parts of Congruent Triangles are Congruent)
Proving segment or angle bisector…? Show triangles are congruent. Parts of bisecting segment or angle are contained in triangles. Prove that those parts are congruent by CPCTC which proves the bisector
Proving lines parallel…? Show triangles are congruent. ANgles contained in triangles are alternate interior, corresponding, or alternate exterior angles of lines. Prove these angles are congruent by CPCTC lines then have to be parallel
Proving lines are perpendicular…? Show triangles are congruent. Angles contained in triangles are formed by the lines are linear pair. Prove those angles are congruent by CPCTC Angles then have to be right angles and lines must be perpendicular
An Altitude of a triangle is…? A segment drawn from any vertex of the triangle, perpendicular to the opposite side, extended outside the triangle if necessary
A Median of a triangle is…? A segment drawn from any vertex of the triangle to the midpoint of the opposite side
If two parallel lines are cut by a transversal then their alternate interior angles are …? Congruent
If two parallel lines are cut by a transversal then their corresponding angles are…? Congruent
If two parallel lines are cut by a transversal then their alternate exterior angles are…? Congruent
If two parallel lines are cut by a transversal then interior angles on the same side of the transversal are…? Supplementary
If two lines form supplementary interior angles on the same side of a transversal then the lines are…? Parallel
An exterior angle of a polygon is…? An angle that forms a linear pair with one of the interior angles of the polygon
If two sides of a triangle are congruent, then…? The angles opposite those sides are congruent
If a triangle is equilateral, then…? It is also equiangular