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If I get a 100%, then I will have an A. What is p? I get a 100% What is q? I will have an A What is the converse? If I have an A, then I got a 100%.

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If I get a 100%, then I will have an A. What is the inverse? If I don’t get a 100%, then I won’t have an A. What is the contrapositive? If I don’t have an A, then I didn’t get a 100% Is the inverse true or false? False, I could get a 98% and still have an A.

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Five times an angle’s supplement is 132 more than the angle. Find the measure of the angle. 5(180 – x) = x + 132 900 – 5x = x + 132 768 = 6x 128 = x

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2 1 7 8 How do you know that: Vertical angle thm Angle 1 is supplementary to angle 2? Definition of a linear pair Angle 7 congruent to angle 1? Vertical angle thm Angle 8 is congruent to angle 2?

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Construct a truth table for (pV~q)Λr pq~q(pV~q)r(pV~q)Λr TTT TTF TFT TFF FTT FTF FFT FFF FFTTFFTTFFTTFFTT TTTTFFTTTTTTFFTT TFTFFFTFTFTFFFTF

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If an animal is a zebra, then it is mammal. What is the inverse? If an animal is NOT a zebra, then it is not a mammal. What is the contrapositive? If an animal is not a mammal, then it is not a zebra. Is the inverse true or false? False, the mammal could be a human.

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What is p? An animal is a zebra What is q? It is a mammal What is the converse? If an animal is a mammal, then it is a zebra. If an animal is a zebra, then it is mammal.

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How do you know that: Given Angle E is congruent to angle EBC? Right angle thm Angle ABC is a straight angle? Assumed from diagram. Angle E is a right angle? C B A DF E

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How do you know that: If 2 angles are straight angles, then they are congruent Segment EF + segment FD = segment ED? Segment addition postulate Angle ABE + angle EBC = 180? Definition of linear pair. Angle ABC is congruent to angle EFD? C B A DF E

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Construct a truth table for (~p ᴠ q)ᴠ~r p~pq(~pVq)r~r(~pVq)V~r TTT TTF TFT TFF FTT FTF FFT FFF FFFFTTTTFFFFTTTT TTFFTTTTTTFFTTTT FTFTFTFTFTFTFTFT TTFTTTTTTTFTTTTT

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How do you know that: Definition of midpoint FD congruent to BC? Transitive property EF congruent to FD? C B A DF E Given: B is the midpoint of segment AC F is the midpoint of segment ED BC is congruent to EF

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How do you know that: Like multiples of congruent segments are congruent F is the midpoint of segment ED? Given ED congruent to AC? C B A DF E Given: B is the midpoint of segment AC F is the midpoint of segment ED BC is congruent to EF

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The sum of twice an angle and its complement is 50 less than the angle’s supplement. Find the measure of the angle’s complement. 2x + 90 – x = 180 – x – 50 x + 90 = -x + 130 2x = 40 x = 20complement = 70˚

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Write as a biconditional: A polygon is an octagon iff it has 8 sides. An octagon is a polygon with 8 sides.

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How do you know that: Given AB + BC = AC? Segment addition postulate AB = BC? Definition of midpoint B is the midpoint of segment AC? C B A Given: B is the midpoint of segment AC

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If a polygon is a triangle, then it has 3 sides. True (definition!) a) Identify p and q b) Is the converse true or false?

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If a polygon is a triangle, then it has 3 sides. a) What is the inverse? b) What is the conclusion? If a polygon is not a triangle, then it does not have 3 sides. it has 3 sides.

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How do you know that: Definition of angle bisector Angle CAB congruent to angle DFE? Like multiples of congruent angles are congruent Angle 1 congruent to angle 2? C B A D F E H G 1 2 3 4 Given: AH and FG are angle bisectors Angle 1 congruent to angle 3

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Construct a truth table for (pΛ~q)ᴠr. pq~q(pΛ~q)r(pΛ~q)Vr TTT TTF TFT TFF FTT FTF FFT FFF FFTTFFTTFFTTFFTT FFTTFFFFFFTTFFFF TFTTTFTFTFTTTFTF

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How do you know that: Subtraction—when congruent angles are subtracted from congruent angles, the differences are congruent. Angle 1 + angle 2 = angle CAB? Angle addition postulate Angle 3 congruent to angle 2? C B A D F E H G 1 2 3 4 Given: Angle CAB congruent to angle DFE angle 1 congruent to angle 4

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2.6 – Proving Statements about Angles Definition: Theorem A true statement that follows as a result of other true statements.

2.6 – Proving Statements about Angles Definition: Theorem A true statement that follows as a result of other true statements.

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