Chapter 2 Theorems Flashcards
Congruent Compliments Theorem
Of two angles are supplementary to the same angle ( or two congruent angles), then the two angles are congruent.
Ex.
Angle1 and angle2 are supplementary. Angle2 and angle3 are supplementary.
Angle1 is congruent to angle3
Linear Pair Theorem
If two angles form a linear pair, then they are supplementary
Right Angle Congruence Theorem
All right angles are congruent
Congruent Compliments Theorem
If two angles are complementary to the same angle (or two congruent angles), then the two angles are congruent.
Ex.
Angle1 and angle2 are complementary. Angle2 and angle3 are complementary.
Angle1 is congruent to angle3.
Common Segments Theorem
Given collinear points A, B, C, and D, arraigned as shown, if segment AB is congruent to segment CD, then segment AC is congruent to segment BD.
.|.____.|.
A B C D
Ex.
Segment AB is congruent to segment CD
Segment AC is congruent to segment BD
Vertical Angles Theorem
Vertical angles are congruent.
Ex. AngleA and angleB are vertical angles
AngleA is congruent to AngleB
Congruent Supplements Theorem
If two congruent angles are supplementary, then each angle is a right angle.
Converse
The statement formed by exchanging the hypothesis and conclusion of a conditional statement
Contrapositive
The statement formed both exchanging and negating the hypothesis and conclusion of a conditional statement
Inverse
The statement formed by negating the hypothesis and conclusion of a conditional statement.
Law of Detachment
If p -> q is a true statement and p is true than q is true.
Law of syllogism
If p -> q and q -> r are true statements, then p-> is a true statement
Theorem:
Congruent angles supps. Then right angles
If two congruent angles are supplementary, then each angle is a right angle
