Bell Work: If you have not turned in your signed syllabus or contract please put it in the basket. Get out your pages from yesterday: 32, 35, 38-42 On.

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Presentation transcript:

Bell Work: If you have not turned in your signed syllabus or contract please put it in the basket. Get out your pages from yesterday: 32, 35, 38-42 On page 32 Complete the boxes on B and C and draw the image on the coordinate plane

Essential Question: How do you go about proving a statement? 1.4 Reasoning and Proof Essential Question: How do you go about proving a statement?

Conjecture – a statement that is believed to be true Inductive reasoning – the process of reasoning that a rule or statement is true because specific cases are true Deductive reasoning – the process of using logic to draw conclusions

Theorem – a statement that you can prove is true using a series of logical steps Counterexample – an example that shows a conjecture to be false Conditional statement – a statement that can be written in the form “If p, then q’ where p is the hypothesis and q is the conclusion

Properties of Equality Addition Property of Equality If a=b, then a + c = b + c Subtraction Property of Equality If a=b, then a - c = b – c Multiplication Property of Equality If a=b, then ac = bc Division Property of Equality If a=b and c ≠ 0, then a/c = b/c Reflexive Property of Equality a = a Symmetric Property of Equality If a=b, then b=a Transitive Property of Equality If a=b and b=c, then a=c Substitution Property of Equality If a=b, then b can be substituted for a in any expression

Use deductive reasoning to solve the equation Use deductive reasoning to solve the equation. Use the properties of equality to justify each step. 1. 14 = 3x – 4 2. 9 = 17 – 4x

Write the statement as a conditional. The bill will pass if it gets two-thirds of the vote in the Senate.

Identify the property of equality that is used in each statement. If x = 2, then 2x = 4 5 = 3a; therefore 3a = 5 If T = 4, then 5T + 7 = 27 If 9 = 4x and 4x = m, then 9 = m.

Linear Pair- a pair of adjacent angles whose non- common sides are opposite rays

The Linear Pair Theorem If two angles form a linear pair, then they are supplementary. 4 3 m<3 + m<4 = 180°

Use a postulate or theorem to find the value of x in each figure. 1. RS = x + 2, ST = 3x – 8, and RT = 5x – 12 2. <RSP = x + 25, <PST = 5x + 10, and <RST = 15x - 10 R P S T R S T

Tear out pages 50 & 54

Homework P. 38 1-6 P. 54 13-15; 17-20