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JRA Geometry Chptr 2
If-then statments, properties, special angles, perpendicular lines, + proofs
| Question | Answer |
|---|---|
| A statement that is usually written in the "if-then" form. It is usually true. | Conditional statement |
| Another name for a conditional statement. | Conditional |
| The two parts of a conditional. | Hypothesis and Conclusion |
| The letter often used to symbolize the hypothesis. | p |
| The letter often used to symbolize the conclusion. | q |
| The most common form of a conditional. | If p, then q. |
| Three other forms of a conditional. | p implies q; p only if q; q if p. If, then, implies, and only if are not part of the hypothesis or the conclusion. |
| A statement formed by interchanging the hypothesis and conclusion of a conditional. It is not always true. | Converse |
| An example that proves a statement is false. | Counterexample |
| A statement combining a conditional and its converse. It is written using if and only if. Both the conditional and its converse must be true. | Biconditional |
| If x-7=10, then x=17. | Addition property of equality |
| If x+7=17, then x=10. | Subtraction property of equality |
| If x/2=9, then x=18. | Multiplication property of equality |
| If 2x=18, then x=9. | Division property of equality |
| If x+5=11 and x=6, then 6+5=11. | Substitution property |
| DE=DE. | Reflexive property |
| If DE=AB, then AB=DE. | Symmetric property |
| If DE=AB, and AB=CF, then DE=CF. This is a specific type of substitution. | Transitive property |
| If M is the midpoint of segment AB, then AM=1/2AB and MB=1/2AB. | Midpoint Theorem |
| If ray BX is the bisector of angle ABC, then the measure of angle ABX=1/2 the measure of angle ABC, and the measure of angle XBC=1/2 the measure of angle ABC. | Angle Bisector Theorem |
| Two angles whose measure have the sum of 90 degrees. | Complementary angles |
| Two angles whose measure have the sum of 180 degrees. | Supplementary angles |
| One of the two complementary angles. | Complement |
| The general measure of an angle's complement. | 90-x |
| One of the two supplementary angles. | Supplement |
| The general measure of an angle's supplement. | 180-x |
| Special angles that are formed when two lines intersect. They are directly across from each other. | Vertical angles |
| Vertical angles are congruent. | Theorem 2-3 |
| Two lines that form right angles. | Perpendicular lines |
| The symbol for perpendicular lines. | An upside-down T |
| All definitions are known as these. | Biconditionals |
| The two conditionals for the definition of perpendicular lines. | If two lines are perpendicular, then they form right angles; If two lines form right angles, then the lines are perpendicular. |
| The biconditional for the definition of perpendicular lines. | Two lines are perpendicular if and only if they form right angles. |
| If two lines are perpendicular, then they form congruent adjacent angles. | Theorem 2-4 |
| If two lines form congruent adjacent angles, then the lines are perpendicular. This is the converse of Theorem 2-4. | Theorem 2-5 |
| If the exterior sides of two adjacent acute angles are perpendicular, then the angles are complementary. | Theorem 2-6 |
| A written list of conclusions made before writing a proof. | Plan of a proof |
| If two angles are supplements of congruent angles (or of the same angle), then the two angles are congruent. | Theorem 2-7 |
| If two angles are complements of congruent angles (or of the same angle), then the two angles are congruent. | Theorem 2-8 |
| Two methods for finding a plan of a proof. | Gather as much information as possible + work backwards |
| A list of statements and reasons that proves a theorem. | Proof |
Created by:
LOSBH47
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