Pythagorean Theorem Theorem

a² + b² = c² a b c p. 20

Distance Formula Theorem

p. 19

Segment Addition Postulate Postulate

If B is between A and C, then AB + BC = AC. A B C  p. 18

Angle Addition Postulate Postulate

If P is in the interior of  ABC, then m  ABP + m  PBC = m  ABC A B C  p. 27   P

midpoint Definition

The midpoint is a point that divides or bisects a segment into two equal segments. If M is a midpoint, then AM = MC. A M C  p. 34

segment bisector Definition

A segment bisector is a line, ray, segment or plane that intersects a segment at its midpoint. A M C p. 34 k 

angle bisector Definition

An angle bisector is a ray that divides an angle into two congruent adjacent angles. 1 p  1   2

Midpoint Formula Theorem

p. 35  M

complementary angles Definition

A pair of angles whose sum is 90° are complementary. 1 p m  1 + m  2 = 90

supplementary angles Definition

A pair of angles whose sum is 180° are supplementary. 1 p m  1 + m  2 = 180

right angle Definition

An angle whose measure is 90° is a right angle. p °

perpendicular lines Definition

Two lines are called perpendicular if they intersect to form a right angle. p. 79

Reflexive Property

For any real number, a = a. p. 96 A B C D

Transitive Property

If a = b and b = c, then a = c. p. 96 A B.. C D.. E F.. If AB = CD and CD = EF, then AB = EF.

Addition Property of Equality Property

If a = b, then a + c = b + c. p. 96 A B C D... If AB = CD, then AC = BD..

Subtraction Property of Equality Property

If a = b, then a  c = b  c. p. 96 A B C D... If AC = BD, then AB = CD..

Substitution Property

If a = b, then a can be substituted for b in any equation or expression. p. 96 Example: If AB = 5 + x and x = 3, then AB = 8.

Right Angle Congruence Theorem Theorem

All right angles are congruent. 1 p  1   2

Congruent Supplements Theorem Theorem

Two angles supplementary to the same angle (or   ’s) are congruent. 1 p If m  1 + m  2 = 180 and m  2 + m  3 = 180, then  1   3.

Congruent Complements Theorem Theorem

Two angles complementary to the same angle (or   ’s) are congruent. 1 p If m  1 + m  2 = 90 and m  2 + m  3 = 90, then  1   3.

Linear Pair Postulate Postulate

If two angles form a linear pair, then they are supplementary. p m  1 + m  2 = 180

Vertical Angles Theorem Theorem

Vertical angles are congruent. 1 2 p. 112  1   2 and  3   4 3 4

Linear Pair of   s Theorem

If two lines intersect to form a linear pair of congruent angles, then the lines are perpendicular. p. 137 g h g h

Corresponding Angles Postulate Postulate

If two parallel lines are cut by a transversal, then corresponding  ’s are . p 1  2 1  2 2

Alternate Interior Angles Theorem Theorem

p. 143 If two parallel lines are cut by a transversal, then alt. int.  ’s are . 1 1  2 1  2 2

Alternate Exterior Angles Theorem Theorem

p. 143 If two parallel lines are cut by a transversal, then alt. ext.  ’s are . 1 1  2 1  2 2

Consecutive Interior Angles Theorem Theorem

p. 143 If two parallel lines are cut by a transversal, then consecutive int.  ’s are supplementary. 1 2 m  1 + m  2 = 180

Perpendicular Transversal Theorem Theorem

p. 143 If a transversal is perpendicular to one of two parallel lines, then it is perpendicular to the other. k j  m j m

Two Lines Perpendicular to Same Line Theorem

p. 157 In a plane, two lines perpendicular to the same line are parallel to each other. k j // m j m

Two Lines Parallel to the Same Line Theorem

p. 157 If two lines are parallel to the same line, then they are parallel to each other. k m // n n m

Triangle Sum Theorem Theorem

p. 196 The sum of the measures of the interior angles of a triangle is 180°. A B C m  A + m  B + m  C = 180

Exterior Angle Theorem Theorem

p. 197 The measure of an exterior angle of a triangle is equal to the sum of the two remote interior angles. A B 1 m  1 = m  A + m  B

Third Angles Theorem Theorem

p. 203 If two angles of one  are  to two angles of another , the third angles are . A B C D E F If  A   D and  B   E, then  C   F

SSS Side-Side-Side Congruence Postulate

p. 212 If three sides of one  are  to three sides of another , then the  ’s are . A B C D E F If,, and, then  ABC   DEF.

SAS Side-Angle-Side Congruence Postulate

p. 213 If two sides of one  are  to two sides of another , and the included  s are , then the  ’s are . A B C D E F If, and  A   D, then  ABC   DEF.

Perpendicular/Right  Theorem (Meyers Theorem) Theorem

p. 157 Perpendicular lines form  right  s. k j m If j  k and m  k, then  1  

ASA Angle-Side-Angle Congruence Postulate

p. 220 If two  s of one  are  to two  s of another , and the included sides are , then the  ’s are . A B C D E F If  A   D,  C   F and, then  ABC   DEF.

AAS Angle-Angle-Side Congruence Postulate

p. 220 If two  s of one  and a non-included side are  to two  s of another  and the corresponding non-included side, then the  ’s are . A B C D E F If  A   D,  C   F and, then  ABC   DEF.

Base Angles Theorem Theorem

p. 236 If two sides of a  are , then the  s opposite those sides are .

Base Angles Converse Theorem Theorem

p. 236 If two  s of a  are , then the sides opposite those  s are .

Hypotenuse-Leg Theorem H-L Theorem

p. 238 If the hypotenuse and a leg of one right  are  to a hyp. and a leg of another rt. , the two  s are . A B C D E F

Perpendicular Bisector Theorem Theorem

p. 265 If a point is on the  bisector of a segment, then it is equidistant from the endpoints of that segment. A B C k P AC = BC

Angle Bisector Theorem Theorem

p. 266 If a point is on the bisector of an angle, then it is equidistant from the sides of the angle. A B C P AP = CP

Circumcenter Theorem

p. 273 The perpendicular bisectors of a triangle intersect in a point that is equidistant from the vertices of the triangle.

Incenter Theorem

p. 274 The angle bisectors of a triangle intersect in a point that is equidistant from the sides of the triangle.

Centroid Theorem

p. 279 The medians of a triangle ( E, D, and F are midpoints) intersect in a point called a centroid. AP = 2 / 3 AD, BP = 2 / 3 BF, CP = 2 / 3 CE A F C E D B P

Orthocenter Theorem

p. 281 The altitudes of a triangle intersect in a point of concurrency called an orthocenter.