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# JRA Geometry Chptr 2

### If-then statments, properties, special angles, perpendicular lines, + proofs

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