8-1 Pythagorean Theorem and the Converse

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8-1 Pythagorean Theorem and the Converse

PYTHAGOREAN THEOREM c b a c a b What side is ALWAYS the c? The HYPOTENUSE!! (Remember it’s across from the 90.) a b a and b are the legs. They can go in any order.

Pythagorean Triples! A “triple” is a set of whole numbers that satisfy the Pythag. Thm. Common Triples: 3-4-5 5-12-13 8-15-17 7-24-25 6-8-10 9-12-15

Example—Find c. c 6 8 It’s a Triple!! 6-8-10 62 + 82 = c2 36 + 64 = c2

Example– Find x 10 7 x2 + 49 = 100 x It’s NOT a Triple!!

Example What is the length of the hypotenuse of triangle ABC? Do the side lengths of triangle ABC form a Pythagorean Triple? Explain.

Word Problem– DRAW A PIC!!!!

Do the numbers form a Pythag. Triple?? (TWAP it out!) Hint: Plug into P. Thm to see if it works 1) 5, 7, 9 2) 10, 24, 26 Explain why!!! Now, Let’s do The “Pythag. Converse”

RULES: c2 < a2 + b2. Acute (< 90) c2 > a2 + b2 RULES: c2 < a2 + b2 Acute (< 90) c2 > a2 + b2 Obtuse (> 90) Remember that c is the longest side! The “c” is in “c”harge!! It tells you the answer. Is it a right, acute or obtuse triangle? 3, 6, 7 72___32+62 49>45 so its obtuse! Try On Own: Is it right, acute, or obtuse? 20,21,28 5,6,8 20,21,29 Answers: Acute 784<841 Obtuse 64>61 Right 841= 841

Be Careful with Rads! Which side is the longest? 4, √23, 8 √23 = 4.8 so 8 is the longest!! What type of triangle is it? 64___16 + 23 (Why is it 23?) 64>39 so it’s obtuse!

Homework Pg. 495-496 # 7 – 31 odd