2. Parts of a Right Triangle A B C Leg Hypotenuse Acute Angle Right Angle Acute Angle R e m e m b e r t h a t t h e h y p o t e n u s e i s a l w a y s t h e l o n g e s t s i d e. That was easy

3. The Pythagorean Theorem The formula looks like this: In a right triangle, the sum of the squares of the lengths of the legs is equal to the square of the hypotenuse. How am I supposed to remember that? Let’s look at a diagram. A B C a b c Let’s look at some examples with actual numbers. 4 35 13a That was easy

4. Pythagorean Theorem Examples Remember the formula. a 2 + b 2 = c 2 6 12 x 16 x 9 11 x That was easy

5. Pythagorean Theorem Word Problems A ladder is placed 5 feet from the foot of a wall. The top of the ladder reaches a point 12 feet above the ground. Find the length of the ladder. 5 12 x On his way to school, Tyrell walked 2 miles east and then 3 miles north. To the nearest hundredth of a mile, what is the direct distance of the school from the house? 2 3 x That was easy

6. Homework Page 617: 6 - 22 Even Numbers

7. Converse of the Pythagorean Theorem If a triangle has sides of lengths a, b, and c, and a 2 + b2 b2 = c2,c2, then the triangle is a right triangle with hypotenuse of length c.c. Determine if the given lengths can be sides of a right triangle. 10 in, 26in, and 24 in YES 11 in, 14in, and 20 in NO 34 in, 16in, and 30 in YES That was easy

8. Forces and Resultants When two forces pull on an object, a resultant is created. Force A Force B Resultant C The resultant is the diagonal of the parallelogram formed by connecting the two forces. What does this have to do with right triangles and the Pythagorean Theorem? Let me show you.

9. Forces, Resultants and the Pythagorean Theorem When two forces pull at right angles to each other, the resultant force is the diagonal of the rectangle formed. Force A Force B Resultant C The diagonal forms a right triangle. If a triangle has sides of lengths a, b, and c, and a 2 + b 2 = c 2, then the triangle is a right triangle with hypotenuse of length c.

10. Problems Involving Forces and Resultants Determine if the forces in each pair are pulling at right angles to each other. 12 lb, 16 lb Resultant force 20 lb YES 22 lb, 19 lb Resultant force 30 lb NO 30 lb, 16 lb Resultant force 34 lb YES That was easy

11. Homework Page 617: 23 – 29 All Questions

12. Pythagorean Triples A Pythagorean Triple occurs when three integers satisfy the equation a2 a2 + b2 b2 = c2.c2. Let’s look at some examples. A BC 3 4 c 12 16 3, 4, 5 or any multiple of 3, 4, 5 5 12 10 24 5, 12, 13 or any multiple of 5, 12, 13 8 15 24 45 8, 15, 17 or any multiple of 8, 15, 17 That was easy

13. Pythagorean Triples Examples Pythagorean Triples that you need to remember are: 3, 4, 5 5, 12 13 8, 15, 17 18 24 x 18 = ( 3 )( 6 ) 24 = ( 4 )( 6 ) Therefore, x = (5)(6) 30 34 x 34 = ( 17 )( 2 ) 30 = ( 15 )( 2 ) Therefore, x = (8)(2) 15 39 x 15 = ( 5 )( 3 ) 39 = ( 13 )( 3 ) Therefore, x = (12)(3) 3, 4, 58, 15, 17 5, 12, 13 That was easy

14. More Pythagorean Theorem Examples Example 1 12 16 x Example b 14 x Example 3 11 6 x Example d 10 18 88 x The length of a rectangle is 16inches and the width is 12 inches. Find the length of the diagonal. The diagonal of a square is 14 inches. Find the length of a side. The sides of an isosceles triangle are 11 inches and the base is 6 inches. Find the height of the triangle. Asi De Facil x

15. Area & Perimeter with the Pythagorean Theorem The diagonal of a square is 21 inches. Find the area of the square. 21 The length of a rectangle is 36inches and the diagonal is 39 inches. Find the perimeter of the rectangle. 39 36 x x x

16. Homework Page 617: 30 - 37 All Questions