Pythagorean Theorem M 08 CG 2 1 1

Pythagorean Theorem � M 08. C-G. 2. 1. 1 Apply the converse of the Pythagorean theorem to show a triangle is a right triangle. � M 08. C-G. 2. 1. 2 Apply the Pythagorean theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions. � M 08. C-G. 2. 1. 3 Apply the Pythagorean theorem to find the distance between two points in a coordinate system.

Pythagorean Theorem Topics: � Sides of a right triangle � Find missing side using a² + b² = c² � Use the Pythagorean Theorem converse � Find the distance between two points in a coordinate system

Wednesday Warm-up 1: find b.

Wednesday Warm-up 1: find b. a² + b² = c² 152 + b 2 = 252 225 + b² = 625 -225 b² = 400 20 Because the numbers 15, 20, and 25 are whole numbers that can form the sides of a right triangle, they are said to be a Pythagorean Triple.

Wednesday warm-up 2: find x. a² + b² = c² 7² + 6² = x² = 9. 2 49 + 36 = x² 85 = x² x = 9. 2 6, 7, and 9. 2 can form the sides of a right triangle, BUT they are not all whole numbers. They do NOT make a Pythagorean Triple.

In a computer catalog, a computer monitor is listed as being 19 inches. This distance is the diagonal distance across the screen. If the screen measures 10 inches in height, what is the actual width of the screen to the nearest inch? Step 1: draw a picture. 10” 19” x” 16. 2” NO: NOT all whole numbers Step 2: solve the problem. Pythagorean Triple? Why or why not? Step 3: answer the question. The screen is 16 inches wide.

Find the perimeter of a right triangle with hypotenuse 17” and leg 5”. 17” � Step 1: Draw a diagram. 5” x” 16. 2” � Step 2: Find the length of the missing side. x 2 + 52 = 172 x 2 + 25 = 289 x 2 = 264 Does this answer make sense? � Step 3: Find the perimeter of the triangle. 16. 2 + 5 + 17 = 38. 2 The perimeter of the triangle is 38. 2 inches.

7. 1 Pythagorean Theorem Converse How do you know if you have a right triangle? Let’s say you have the length of the sides of a triangle. What would you do to determine whether it was a right triangle? 10 cm 6 cm 8 cm

7. 1 Converse of the Pythagorean Theorem If the sum of the squares of the lengths of the two shorter sides of a triangle is equal to the square of the length of the longest side, then the triangle is a right triangle. If a² + b² = c² , then the triangle is a right triangle. Whoa! Did you get that? Break it down, step by step.

Converse If the sum of the squares of the lengths of the two shorter sides of a triangle Which sides are the shorter sides? 6 and 8

Converse is equal to the square of the length of the longest side, then the triangle is a right triangle. Which is the long side? 10 is the long side

Converse So…if a² + b² = c² , then the triangle is a right triangle. 6² + 8² = 10² 36 + 64 = 100 ____ = 100 Is it true? Because 6 -8 -10 is a set of whole numbers that can form a right triangle, it is a Pythagorean Triple. Yes, the triangle is a right triangle!

Converse Is this triangle a right triangle? Apply the converse.

Converse Short sides: 6 and 9 Long side: 15 Substitute into the Pythagorean Theorem to see if it works! a² + b² = c² 6² + 9² = 15² 36 + 81 = 225 ______ = 225

Converse 36 + 81 = 225 117 ≠ 225 That means it is not a right triangle! Is 6 -9 -15 a Pythagorean Triple? 6, 9, and 15 are whole numbers but they cannot form a right triangle. It is not a Pythagorean Triple.

Seth made a small table for his workroom. The sides of the table are 36" and 18". If the diagonal of the table measures 43", is the table rectangular? A table which is "rectangular" has right angles at the corners. 36" ? 18" 43" 362 + 182 = 432 1296 + 324 = 1849 1620 ≠ 1849 The angle is NOT a right angle. The table is NOT rectangular.

Independent work - Converse � Do worksheet Pythagorean Theorem Word Problems J #1 -5. Show all steps. (Remember to label the answer. ) � Do Converse 1 Pythagorean Theorem worksheet #10 - 15. Show your steps. Say yes or not as to whether you have a right triangle or not.

Reminder! This week � Class on Friday, May 29 at usual time ◦ Core classes from 8: 00 -10: 00 at usual times ◦ Follow your Monday UA schedule. � Today, follow your usual Wednesday schedule. Next week � Regular classes Monday and Wednesday, June 1 & 3. � Team awards assembly on Teams Thursday, June 4 at 9: 00 AM. (Invitation from Mr. Barnas. )

Reminder! � Office hours are held Tuesday and Thursday at the usual time. Come and get help. � Complete your math benchmark by Friday, June 5. � All assignments for Q 4 are on Mrs. Lasak’s website (homework page. ) � Work assigned after May 1 are also on Google Classroom. � All 4 th marking period work must be turned in by Friday, June 5.