~adapted by Walch Education  The Pythagorean Theorem is often used to find the lengths of the sides of a right triangle, a triangle that includes one.

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Presentation transcript:

~adapted by Walch Education

 The Pythagorean Theorem is often used to find the lengths of the sides of a right triangle, a triangle that includes one 90˚ angle.  By the way, Geometry includes many statements. Once a statement has been shown to be true, it is called a theorem.

 The sum of the squares of the lengths of the legs (a and b) of a right triangle is equal to the square of the length of the hypotenuse (c). a 2 + b 2 = c 2

If the sum of the squares of the measures of two sides of a triangle equals the square of the measure of the longest side, then the triangle is a right triangle.

Paragraph proofs are statements written out in complete sentences in a logical order to show an argument. Two-column proofs include numbered statements and corresponding reasons that show the argument in a logical order. Flow proofs are a graphical method of presenting the logical steps used to show an argument. In a flow proof, the logical statements are written in boxes and the reason for each statement is written below the box.

 We will write a two column proof in class for this… and maybe a paragraph proof, Ok, why not?! A flow proof as well.

 Find the length of the altitude, x, of

 Use corresponding sides to write a proportion containing x   (x)(x) = (10)(18)  x 2 = 180 therefore

~Ms. Dambreville