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55 Cards in this Set
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Plane Postulates

1. A line, a plane, and space contain infinite points.
2. For any two points there is exactly one line containing them 3. For any three noncollinear points there is exactly one plan containing them 4. If two points are in a plane, then the line containing them is in the plane 5. If two planes intersect, then they intersect at exactly one line 

Segment Addition Postulate

If Q is between P and R then PQ+QR= PR


Angle Addition Postulate

If F is in the interior of <CDE, then m<CDF + m<FDE = m<CDE


Definition of Congruent

Congruent segments are segments that have the same length. The same applies to angles with angle measure.


Definition of Midpoint

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


Definition of a bisector

A bisector of a segment is the point, part of a line, or plane that divides the segment into two congruent segments. The bisector of an angle is a ray in the interior of the angle that divides the angle into two congruent angles.


Midpoint Postulate/Angle Bisector Posulate

A segment has exactly one midpoint. An angle has exactly one bisector.


Definition of a triangle

A triangle is a figure formed by three segments joining three non collinear points.


Theorem about Angle and Segment Congruence

Congruence of segments and angles is reflexive, symmetric, and substitutive.


Definition of complementary angles

Complementary angles are two angles whose measures have a sum of 90


Definition of Supplementary Angles

Supplementary angles are two angles whose measures have a sum of 180.


Definition of Linear Pair

A linear pair of angles is a pair of adjacent angles with the two noncommon sides on the same line.


Linear Pair Posulate

Two angles that form a linear pair are supplementary.


Theorem about linear pairs

The sum of the measures of the angles in a linear pair is 180.


Vertical Angle Theorem

If two angles are vertical angles, then they are congruent.


Definition of Perpendicular Lines

Perpendicular lines are two lines that intersect at right angles


Theorem about perpendicular lines

Through a given point on a line, there is exactly one line in the plane perpendicular to the given line.


Definition of a Perpendicular Bisector

A perpendicular bisector of a segment is a line, segment, ray, or plane that is perpendicular to the segment and bisects it.


Information that May Be Assumed From a Diagram

1. Straightness of lines
2. Betweenness of points 3. Collinearity of points on a line, coplanarity of points 4. Intersection of lines 5. Relative locations (interior, exterior, opposite) 6. Adjacency, nonadjacency of angles 7. Existence of the figures shown 

Information that May Not be Assumed From a Diagram

1. Congruence of segments or angles
2. Measures of segments or angles 3. Relative sizes of segments and angles 4. Midpoint of a segment or bisector of an angle 5. Perpendicular lines or right angles 6. Nonintersecting lines 7. Special types of figures 

Theorem about right angles

All right angles are congruent


Midpoint Theorem

The midpoint M of line segment AB divides AB so that AM=1/2 AB


Angle Bisector Theorem

If ray BD is the bisector of <ABC, then m<ABD=1/2 m<ABC


Common Segment Theorem

1. If AB is congruent to CD, then AC is congruent to BD
2. If AC is congruent to BD, then AB is congruent to CD 

Theorem about congruent adjacent angles

If two lines form congruent adjacent angles, then they are perpendicular


Theorem about points and perpendicular lines

Only one perpendicular line can be drawn from a point to a line


Common Angle Theorem

1. If <AOB is congruent to <COD, then <AOC is congruent to <BOD.
2. If <AOC is congruent to <BOD, then <AOB is congruent to <COD. 

Congruent Complements Theorem

Two angles that are complementary to the same angle (or to congruent angles) are congruent.


Congruent Supplements Theorem

Two angles that are supplementary to the same angle (or to congruent angles) are congruent.


Methods of Proving an Angle a Right Angle

1. Prove that it has a measure of 90.
2. Prove that it is formed by perpendicular lines. 3. Prove that it forms a linear pair with a right angle. 

Definition of parallel planes

Parallel planes are planes that do not intersect.


Definition of parallel lines

Parallel lines are coplanar and do not intersect.


Definition of skew lines

Skew lines are lines that are not coplanar and do not intersect.


Theorem about parallel planes

If two parallel planes are cut by a third plane, the lines of intersection are parallel.


Definition of transversal

A transversal is a line that intersects two coplanar lines in two different points. It forms eight angles.


Definition of alternate interior angles

Alternate interior angles are two nonadjacent interior angles on opposite sides of the transversal. There are two pairs of alternate interior angles.


Definition of alternate exterior angles

Alternate exterior angles are two nonadjacent exterior angles on opposite sides of the transversal. There are two pairs of alternate exterior angles.


Definition of sameside interior angles

Sameside interior angles are two interior angles on the same side of the transversal. There are two pairs of sameside interior angles.


Definition of corresponding angles

Corresponding angles are two non adjacent angles on the same side of the transversal such that one is an exterior angle and the other is an interior angle. There are four pairs of corresponding angles.


Postulate about corresponding angles (know converse)

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


Theorem about alternate interior angles (know converse)

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


Theorem about alternate exterior angles (know converse)

If two parallel lines are cut by a transversal then alternate exterior angles are congruent.


Theorem about sameside interior angles (know converse)

If two parallel lines are cut by a transversal, then sameside interior angles are supplementary.


Theorem about perpendicular lines being parallel

In a plane, two coplanar lines perpendicular to the same line are parallel.


Theorem about transitive parallel lines

Two lines parallel to a third lines are parallel to each other.


Postulate about parallel lines and a point not on the line

Given a line L and a point P not on line L, there exists one and only one line through P parallel to L.


Angle Sum Theorem for Triangles

The sum of the measures of the angles of a triangle is 180.


Corollary about equilateral triangles

The angles of an equiangular triangle each have a measure of 69.


Corollary about right triangles

The acute angles of a right triangle are complementary.


The Exterior Angle Theorem

The measure of an exterior angle of a triangle is equal to the sum of the measures of its two remote interior angles.


Third Angle Theorem

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


Polygon Names

4Quadrilateral
5Pentagon 6Hexagon 7Heptagon 8Octagon 9Nonagon 10Decagon 

Theorem about polygon angle sum

The sum of the measures of the angles of a convex polygon of n sides is ( n  2 ) 180


Corollary about regular polygons

The measure of each angle of a regular polygon of n sides is ( n  2 )( 180 ) / n


Theorem about polygon exterior angle sum

The sum of the measures of the exterior angles of a convex polygon is 360.
