Conditional statement:

Transcription

1 Conditional statement: Hypothesis: Example: If the sun is shining, then it must be daytime. Conclusion: Label the hypothesis and conclusion for each of the following conditional statements: 1. If a number is a whole number, then it is an integer. 2. You will get hurt if you jump off a building. 3. A number is divisible by 3 if it is divisible by 6. Write a conditional statement for each of the following: 4. The midpoint of a segment bisects the segment. Eighteen-year-olds are eligible to vote. Conditional Converse True or False? If an animal is a cat, then it has four legs. If an angle has a measure less than 90, then it is acute. Your name is Michael Phelps if you swim fast.

2 6. What s wrong with this? Conditional: If two angles add up to 90 then they are complimentary. Two angles are complimentary if they add up to Write a conditional and its converse for: A triangle with no congruent sides is a scalene triangle. Conditional: Biconditional: 9. Conditional: If Lindsay takes photos for the yearbook, then she will not play soccer. Biconditional: A biconditional is true if and only if 10. Conditional: A figure is a decagon if it has 10 sides. Biconditional: True or False? 11. Biconditional: m ABC m CBD if and only if BC is an angle bisector of Conditional: True or False? True or False? So the original biconditional statement is ABD. B A C D 12. Biconditional: a = 4 and b = 3 if and only if ab = 12. Conditional: True or False? True or False? So the original biconditional statement is

3 Addition property of equality Subtraction property of equality Multiplication property of equality Division property of equality Reflexive property of equality Symmetric property of equality Transitive property of equality Substitution property of equality Distributive property Properties of equality (p. 136) Identify the property: 1. If AB = CD, then AB + BC = CD + BC. 2. m A m A. 3. If X Y and Y Z, then X Z. x 4. If 5, then x = If XY + CD = 30 and XY = 12, then 12 + CD = If A B, then B A. 7. If x 18 = 36, then x = If 88 = 2x, then 44 = x. 9. If 6n = 3(n 12) + 4n, then 6n = 3n n. 10. If x + 32 = 18, then x = If the Chiefs beat the Raiders and the Raiders beat the Broncos, then the Chiefs should beat the Broncos.

4 12. Solve the equation. Write a justification for each step. 3x + 6(x + 3) = 5x Write a 2-column proof to verify that if 5 x 1 8 0, 2 then x = The formula to convert a Fahrenheit temperature to Celsius is C ( F 32) 9. Solve this equation for F. Write a justification for each step. 1 Given: Prove: x = 6

5 Postulate Segment addition postulate: Used in proofs: 1. Given: BC = DE Prove: AB + DE = AC 1. BC = DE Finish solving. Write a justification for each step. D E F 3x DE + EF = DF Seg. Add. Post. 3. AB + DE = AC Given: PR QS Prove: PQ RS 1. PR QS PR = QS PQ + QR = PR QR + RS = PR 4. Segment Addition Postulate 6. PQ + QR = QR + RS Subtraction prop. of = Definition of congruent segments

6 4. Given: B is the midpoint of AC and AB EF Prove: BC EF. 1. B is the midpoint of AC Given AB CD Given: Prove: 2AB = EF 1. AB CD and AB + CD = EF 1. A E B C D F 2. AB = CD AB + CD = EF Substitution 6. Given: AB DE B is the midpoint of AC. E is the midpoint of DF. Prove: BC EF 1. B is the midpoint of AC E is the midpoint of DF 1. Given Definition of Midpoint 3. AB DE BC DE BC EF 4.

7 Angle addition postulate: Theorem A statement that can be proven true. Linear Pair Theorem: Given: Prove: A C and and B B are complimentary, and are complimentary A C 1. A and B are complimentary m A m B A C def. of angles subst. prop. of = Prove the Linear Pair Theorem: Given: and form a linear pair Prove: 1 and 2 are supplementary def. of straight angle 3. m 1 m 2 m ABC substitution

8 Given: Prove: 1 and are supplementary, and 2 and 3 are supplementary subtraction prop. of = Right Angle Congruence Theorem: Let s prove that theorem: Given: and Prove: are right angles Given: 2 3 Prove: are supplementary 1 and m 2 m Linear Pair Theorem def. of supp. angles m 1 m

9 Given: BX bisects and m XBC 45 Prove: ABC is a right angle ABC 1. BX bisects ABC def. s 4. m XBC m ABX angle add. post Given: BAC is a right angle, and m 2 m 3 Prove: 1 and 3 are complimentary 1. BAC is a right angle angle add. post substitution m 2 m 3 6. m 1 m

10 2-6 worksheet: Properties Identify each property and fill in the blanks. 1. If MN = CD and CD = XY, then MN =. 11. If AB + AB = AC, then 2(AB) = AC 2. If AB + CD = 15 and AB = 6, then 6 + CD = If AB = CD then AB XY = CD XY 3. XY + XY = 13. If m A 140 then m A If ABC DEF then DEF ABC 14. ABC ABC Y Y 6. If A B and B C then 7. If m X 91 then 2(m X ) 1 If m XYZ m ABC and m ABC m DEF m RST then m XYZ m DEF m RST 16. If 5(m XYZ ) m ABC then 1 m XYZ (m ABC) 5 8. If AB = CD then CD = AB 17. If m C 32 then 2(m C) 9. If m 1 35 then m If ABC XYZ then XYZ ABC 10. If m R 40 then 10 + m R 19. If m A m B 80 and m B 3 then m A If m XYZ 90 and m ABC m DEF 90 then m XYZ m ABC m DEF