To be a right triangle or not to be, that is the question!

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Presentation transcript:

To be a right triangle or not to be, that is the question! Pure Genius To be a right triangle or not to be, that is the question!

I’m just conversely saying… Converse of the Pythagorean Theorem The converse of a conditional statement is formed by interchanging the hypothesis and conclusion of the original statement. In other words, the parts of the sentence change places. The words "if" and "then" do not move. If…Then statement. Conditional: If the basket was made, then the ball was shot. (This result is obvious) Converse: If the ball was shot, then the basket was made. (You must prove this statement!) ** It is important to remember that the converse does NOT necessarily have the same truth value as the original conditional statement.

The Converse of the Pythagorean Theorem states: Confused? The Converse of the Pythagorean Theorem states: “If a2 + b2 = c2, then the triangle is a right triangle.” So lets prove it! Determine whether the triangle with the given side lengths will result in a right triangle? 9, 12, 15 24,45,51 9,16,25 8,8,11

Now You Try! Orville and Jerry want to put a custom made, round table in their dining room. The table top is made of glass with a diameter of 85 inches and sits on top of a black pedestal base. The front door is 36 inches wide and 80 inches tall. Orville thinks it will fit through the door, but Jerri does not. Who is correct, and why?

Lets review the Converse Theory If a2 + b2 = c2 and this is a right triangle, then the Pythagorean Theorem can be used to determine if the table will go through the door. 80, 36, 85. 362 + 802 = 852 1296 + 6400 = 7225 7696 Door opening=7225 table Diameter. Door opening is larger so yes it will fit! 80 “ 36” 85” Diameter

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