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### 22 Cards in this Set

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• Back
 What is a conditional statement? A pair of related statements used to draw conclusions What is a converse? Formed by interchanging the hypothesis and conclusion. b->a The statement may be true or false. What is a contrapositive? Formed by interchanging its hypothesis and conclusion and denying both. not b->not a The statement is always true. What is an inverse? Formed by denying both its hypothesis and conclusion. not a->not b When is a statement not valid? A statement is not valid when it is the converse or inverse of the first statement. What is a statement valid? A statement is valid when it is the contrapositive of the first statement. What are the premises? The premises are all of the statements that come before the conclusion. What is a syllogism? A syllogism is a situation in which the conclusion of the first is the same as the hypothesis of the second. a->b b->c What is a theorem? A conclusion derived from a number of premises. What is the midpoint theorem? If M is midpoint of AB, then AM=1/2AB and MB=1/2AB What is the angle bisector theorem? If BX is bisector of angle ABC, then ABX=1/2ABC and XBC=1/2ABC What are the reasons used in proofs? 1. Given information 2. Definitions 3. Postulates 4. Theorems that have already been proved What are complementary angles? 2 angles whose measures have the sum of 90 degrees What are supplementary angles? 2 angles whose measures have the sum of 180 degrees What are vertical angles? 2 angles such that the sides of one angle are opposite rays to the sides of the other angle. When two lines intersect, they form two pairs of vertical angles. (opposite angles) What is theorem 2-3? Vertical angles are congruent What are perpendicular lines? Two lines that intersect to form right angles What is theorem 2-4? If two lines are perpendicular, then they form congruent adjacent angles What is theorem 2-5? If two lines form congruent adjacent angles, then the lines are perpendicular What is theorem 2-6? If the exterior sides of two adjacent acute angles are perpendicular, then the angles are complementary. What is theorem 2-7? If two angles are supplements of congruent angles (or the same angle) then the two angles are congruent What is theorem 2-8? If two angles are complements of congruent angles (of the same angle), then the two angles are congruent