# 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%.

## Presentation on theme: "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%."— Presentation transcript:

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%.

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.

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

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?

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

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.

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.

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

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

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

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

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

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˚

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

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

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?

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.

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

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

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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