If a quadrilateral is a square, then it has 4 right angles. What is p? A quad is a square What is the conclusion? It has 4 right angles What is the converse?

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Presentation transcript:

If a quadrilateral is a square, then it has 4 right angles. What is p? A quad is a square What is the conclusion? It has 4 right angles What is the converse? If a quadrilateral has 4 right angles, then it is a square.

What is the inverse? If a quad is not a square, then it does not have 4 right angles What is the contrapositive? If a quad does not have 4 right angles, then it is not a square. Is the inverse true or false? False, it could be a rectangle. If a quadrilateral is a square, then it has 4 right angles.

m  w ~r  ~w p  m What conclusion can you draw? p  r (p  m  w  r) OR ~r  ~p (~r  ~w  ~m  ~p)

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

Given: Diagram as shown. Prove: angle 1 congruent angle StatementsReasons 1. <1 & <2 are right <s1. Given (assumed from diagram is ok) 2. <1 = <22. Right angle Thm (if 2 angles are right <s, then they are congruent) StatementsReasons 1. <1 & <2 are right <s1. Given (assumed from diagram is ok) 2. <1 & <2 are both 90˚ 2.Def right angle 3. <1 = <23. Def congruent angles

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.

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

Given: Diagram as shown. Prove: angle BAT congruent angle CAR C A R B T StatementsReasons 1. <CAR & <BAT are straight <s 1. Assumed from diagram 2. <CAR = <BAT2. if 2 angles are straight <s, then they are congruent StatementsReasons 1. <CAR & <BAT are straight <s 1. Assumed from diagram 2. <CAR & <BAT are both 180˚ 2.Def straight angle 3. <CAR = <BAT3. Def congruent angles

r  w ~t  ~s a  r t  a What conclusion can you draw? s  w (s  t  a  r  w) OR ~w  ~s (~w  ~r  ~a  ~t  ~s)

If an angle measures 100˚, then it is NOT acute. What is the inverse? If an angle is not 100˚, then it is acute. What is the contrapositive? If an angle is acute, then it doesn’t measure 100˚. Is the inverse true or false? False.Counterexample? 150˚ (a 150˚angle is not 100˚, but is also not acute.)

What is the hypothesis? An angle measures 100˚ What is the conclusion? It is not acute What is the converse? If an angle is not acute, then it measures 100˚ If an angle measures 100˚, then it is NOT acute.

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