1. Things to do: ♥Make a new note book ♥Get out your homework (triangle worksheet)

2. BOE “Buried Treasure” Day 1 These notes go with Worksheet #1, which is Practice 5.4 on one side and Practice 12.3 on the other.

3. The Basics In a right triangle, there are 2 legs and a hypotenuse. –The point where the two legs meet is a right angle –The side across from the right angle is the longest side and it is called the hypotenuse. leg hypotenuse Right angle

4. The legs are a and b, the hypotenuse is c. a b c Pythagorean Theorem a 2 + b 2 = c 2 The formula says that if you square the legs and add them together, you will get the length of the hypotenuse, squared.

5. Try this Find x 3 in. 4 in. x 3 2 + 4 2 = x 2 9 + 16 = x 2 25 = x 2 5 in. = x and -5 in. = x (x = 5 is the answer that will work in this problem) 5 mi. 11 mi. x mi. 5 2 + 11 2 = x 2 25 + 121 = x 2 146 = x 2 12.08 mi = x and -12.08 mi = x (x = 12.08 is the answer that will work in this problem)

6. What if we needed the measure of one of the legs? find x 12 ft. x 13 ft. a 2 + b 2 = c 2 x 2 + 12 2 = 13 2 x 2 + 144 = 169 x 2 = 25 x = 5 ft. Try This 4 mi. x mi. 15 mi. a 2 + b 2 = c 2 x 2 + 4 2 = 15 2 x 2 + 16 = 225 x 2 = 209 x = 14.46 mi.

7. Pythagorean Inequalities when c is the longest side of a triangle, you can tell if the triangle is acute, obtuse or right by using the following: acute: c 2 < a 2 + b 2 obtuse: c 2 > a 2 + b 2 right: c 2 = a 2 + b 2

8. Try this Determine whether the triangle is right, acute or obtuse. 1. 7, 3, 6 3 2 + 6 2 7 2 9 + 36 49 45 49 since the hypotenuse is larger than the square of the legs, it is an obtuse triangle. < ? ? 2. 14, 52, 49 14 2 + 49 2 ? 52 2 196 + 2401 ? 2704 2597 < 2704 Obtuse Triangle

9. Just for fun What is the length of a diagonal of a square with side lengths of 10 units? –Step 1: draw it. –Step 2: label it. –Step 3: set up an equation –Step 4: does my answer make sense? 10 x 10 2 + 10 2 = x 2 100 + 100 = x 2 200 = x 2 14.14 ≈ x

10. Try this What is the length of a diagonal of a square whose side lengths are 5♥? 1. draw it 2. label it 3. set up an equation 4. solve 5. does the answer make sense? 5 x 5 5 5 5 2 + 5 2 = x 2 25 + 25 = x 2 50 = x 2 7.07♥ ≈ x

11. Assignment Practice 5.4 (don’t do #16) Practice 12.3 (all)