Warm Up Simplify the square roots

Sections 7.1-7.2 Pythagorean Theorem and its Converse Objective: To find missing sides of right triangles; to determine if a triangle is a right triangle.

Pythagorean Theorem Where a and b are the legs of the right triangle and c is the hypotenuse. c a b

Use the Pythagorean Theorem to solve for the variable Use the Pythagorean Theorem to solve for the variable. Write your answer in reduced radical form and decimal form. 8 y 17 2.) 15 36 x 1.) 82 + y2 = 172 152 + 362 = x2 64 + y2 = 289 225 + 1296 = x2 y2 = 225 1521 = x2 y = 225 y = 15 39 = x

Pythagorean Triple A set of three positive integers a, b, and c that satisfy the equation Pythagorean Triples: 3, 4, 5 5, 12, 13 8, 15, 17 7, 24, 25 And any multiple of the list above (p.435)

The given lengths are two sides of a right triangle The given lengths are two sides of a right triangle. All three sides of the triangle form a Pythagorean Triple. Find the length of the third side and tell whether it is a leg or hypotenuse. 1.) 40 and 41 2.) 12 and 35 3.) 63 and 65 122 = 144 632 = 3969 402 = 1600 352 = 1225 652 = 4225 412 = 1681 Sum is 1369, which is 372 Difference is 256, which is 162 Difference is 81, which is 92 Third side is 9. It’s a leg. Third side is 37. It’s a hypotenuse. Third side is 16. It’s a leg.

Converse of Pythagorean Theorem : Right Triangle : Acute Triangle : Obtuse Triangle

Decide whether the numbers represent the side lengths of a triangle Decide whether the numbers represent the side lengths of a triangle. If they can, classify the triangles as right, acute, or obtuse. 1.) 20, 21, 28 2.) 15, 36, 39 3.) 14, 48, 50 20+21>28 21+28>20 20+28>21 15+36>39 36+39>15 15+39>36 14+48>50 48+50>14 14+50>48 282 ? 202 + 212 392 ? 152 + 362 502 ? 142 + 482 784 ? 400 + 441 1521 ? 225+1296 2500 ? 196+2304 784 < 841 1521 =1521 2500 =2500 acute right right

Area of a triangle Area = ½ bh, where the base and height are perpendicular to each other. h h b b

Find the area of the triangle given A = ½ bh 12 cm 10 ft. 7 ft. 8 cm 122 = a2 + 42 144 = a2 + 16 128 = a2 A = 35 ft2 A = 45.2 cm2 11.3 = a

Find the unknown side length. 2.) x 1.) x 2 = x2 + X2 + X2 = ( )2 2x2 = 64(2) 19 = x2 + 7 2x2 = 128 12 = x2 x2 = 64 x = x = 8

Homework Textbook pages 430-432 #3-25 every other odd Textbook page 438 #3-25 every other odd