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1 1. Grab board/marker for your group 2. Do WarmUp below TP bisects VS and MR. VM is congruent to SR. MP = 9, VT = 6 Perimeter of MRSV = 62 V T S Find VM. M P R
2 Paragraph Proof D (2x) x 60 A B C Given: Diagram Prove: Angle DBC is congruent to Angle E E According to the diagram, Angle ABC is a straight angle. Therefore, 2x + x = 180 3x = 180 x = 60 Since Angle DBC = 60 and Angle E = 60, the angles are congruent.
3 Paragraph Proof 1 Given: Angle 1 is acute Angle 2 is acute Conclusion: Angle 1 is congruent to Angle 2 This conclusion cannot be proved. For example, if mangle 1 = 20 and mangle 2 = 30, they are both acute but Angle 1 is not congruent to Angle 2. (Counterexample)
4 Paragraph Proof D Given: Angle D is 90 Angle E is obtuse Prove: Angle D is congruent to Angle E E This conclusion can be proved false. Since Angle E is obtuse, its measure is greater than 90. Since Angle D and Angle E have different measures, they are not congruent.
5 On Your Own: Do p.37 #2 and #3 in Boss-Secretary Format
6 Conditional Statements I CAN Write conditional, converse, and biconditional statements
7 Conditional Statements A conditional statement is written in the form if p, then q. If a given condition is met (if p), then another condition is true or an event will happen (then q). The if-clause is the hypothesis; the then-clause is the conclusion.
8 Conditional Statements Ex 1.) If you don t do your homework, then p - Hypothesis you will get lunch detention. q - Conclusion Rewrite the statements in if-then form: Ex 2.) Every multiple of 4 is also a multiple of 2. If a number is a multiple of 4, then it is a multiple of 2. True or False? True
9 Conditional Statements Ex. 3) x 2 144, x 12 If x 2 144, then x 12 True or False? False why? Counterexample: b g
10 Logical Order When given several related conditional statements, you must put them in logical order. The conclusion of one statement will flow into the hypothesis of the next.
11 Logical Order Put the following if-then statements in order A. If Cameron graduates with a degree, then he will make a lot of money. B. If Cameron studies hard, then his grades will be good. C. If Cameron makes a lot of money, then he will be able to buy a new car. D. If Cameron attends college, then he will graduate with a degree. E. If Cameron has good grades, then he will be able to attend college. Logical Order: B. If Cameron studies hard, then his grades will be good. E. If Cameron has good grades, then he will be able to attend college. D. If Cameron attends college, then he will graduate with a degree. A. If Cameron graduates with a degree, then he will make a lot of money. C. If Cameron makes a lot of money, then he will be able to buy a new car.
12 Logical Order Ex. 2 Put the statements in logical order. A. If a shape is a square, then it is a rhombus. B. If a shape is a parallelogram, then it is a quadrilateral. C. If a shape is a quadrilateral, then it is a polygon. D. If a shape is a rhombus, then it is a parallelogram. A. If a shape is a square, then it is a rhombus. D. If a shape is a rhombus, then it is a parallelogram. B. If a shape is a parallelogram, then it is a quadrilateral. C. If a shape is a quadrilateral, then it is a polygon.
13 Inverse - Converse - Contrapositive What is the Inverse? The inverse of a conditional statement is formed by negating the hypothesis and the conclusion. The sentence if p, then q becomes if not p, then not q. State the inverse of the following conditional statements: Ex. 1) If it is sunny today, then Julie will go running. Inverse If it is not sunny today, then Julie will not go running
14 Converse What is the converse? The converse of a conditional statement is formed by switching the places of the hypothesis and conclusion. The sentence if p, then q becomes if q, then p.
15 Converse State the converse of the if-then statements: Ex. 1) If a polygon has five sides, then it is a pentagon. p - hypothesis q - conclusion Converse If a polygon is a pentagon, then it has five sides. q - conclusion p - hypothesis True or False? True
16 Converse Ex. 2) If two lines are perpendicular, then they intersect. Converse If two lines intersect, then they are perpendicular. True or False? False Why? Counterexample -
17 Converse Ex. 3) If a college football team wins the Big Ten Conference then they will play in a bowl game. Converse If a college football team plays in a bowl game then they won the Big Ten Conference. True or False? False Why? Counterexample - There are many other teams that play in bowl games!
18 Converse Ex. 4) If you get an A on the final exam then you will get an A in Advanced Geometry. Converse If you get an A in Advanced Geometry then you got an A on the final exam. True or False? False Why? Counterexample - The final exam is only 15% of your grade!
19 Converse Ex. 5) If three points are collinear then they lie on the same line. Converse If three points lie on the same line then they are collinear. True or False? True!
20 Homework p. 37 #4 7, 9 p. 42 #2 5, 8 12, 14
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