- Right Angle Triangles & Pythagorean Theorem - Approximately January 6 th – January 15 th

This unit will help you develop an understanding of Pythagorean’s Theorem and when to apply it. This will help you prepare for Trigonometry in the later grades. We will learn how to work with: - Right Angle Triangles - Pythagorean Theorem

What Is It?? - A formula that explains the relationship between the 3-sides of a right- angle triangle Pythagorean Theorem. ( ). Uploaded by Donna Roberts to Oswego City School District Regents Exam Prep Center. Available online at:

What Is It?? a 2 + b 2 = c 2 -a & b represent the shorter sides or “legs” of the triangle -c represents the longest side or “hypotenuse” Pythagorean Theorem. ( ). Uploaded by Donna Roberts to Oswego City School District Regents Exam Prep Center. Available online at:

Ways to Represent - Symbolically a 2 + b 2 = c 2 -Linguistically “In any right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs” Pythagorean Theorem. ( ). Uploaded by Donna Roberts to Oswego City School District Regents Exam Prep Center. Available online at:

Ways to Represent - Pictorially (a) 2 +(b) 2 = (c) 2 (3) 2 +(4) 2 = (5) = 25

Example 1 a 2 + b 2 = c 2 (8) 2 +(6) 2 = c 2 (8x8) +(6x6) = c = c = c 2 10 = c Pythagorean Theorem. ( ). Uploaded by Donna Roberts to Oswego City School District Regents Exam Prep Center. Available online at: 6 8

Example 2 a 2 + b 2 = c 2 A triangle has side lengths of 6, 7, & 10, is it a right triangle? *Remember, the longest side MUST be the hypotenuse, so c = 10. (6) 2 +(7) 2 = (10) 2 (6x6) + (7x7) = (10x10) = = 100

Example 3 a 2 + b 2 = c 2 a 2 +(9) 2 = (15) 2 a 2 +(9x9) = (15x15) a = 225 a – 81 = a 2 = 144 a = 12 Pythagorean Theorem. ( ). Uploaded by Donna Roberts to Oswego City School District Regents Exam Prep Center. Available online at:

January 8 th - Your next hand-in day is Wednesday, January 15 th - Solve for the length of the missing hypotenuse in a triangle with legs of 7 feet and 2 feet.

a 2 + b 2 = c 2 (7) 2 +(24) 2 = c 2 (7x7) +(24x24) = c = c = c 2 25 = c 7 24 x

4 3 x What is the length of the diagonal of a rectangle of length 3 and width 4?

x

Complete Questions 3-6 on pg 34 of your textbook.

January 9 th - Your next hand-in day is Wednesday, January 15 th - Solve for the variable x. Please show all your work x 12 13

January 10th - Your next hand-in day is Wednesday, January 15 th - Solve for the length of the missing leg in a triangle with side lengths of 7feet and 2 feet.

January 13th - Your next hand-in day is Wednesday, January 15 th - Shayla’s gnome broke it’s legs & can no longer climb the stairs onto the porch. To help him, Shayla decides to build a ramp. The height from the ground to the top of the stairs is 4 feet. The stairs extend 5 feet in front of her house. How long will her ramp be to accommodate these measurements?

January 14th - Your next hand-in day is Wednesday, January 15 th - Jake is changing the shingles on his roof. He has a 17 foot ladder but can only set it up 8 feet away from the house as he doesn’t want to damage his mom’s flower bed. What is the maximum possible height of Jake’s roof while still having his ladder reach from that distance?

3 4 x 10 January 16th - Hand In Day -

Short Unit Project -Find 5 corners of things in the school (any type of corners, try to be unique!) -Room corners, Desks, Picture Frames, Etc -Measure side lengths (legs & hypotenuse) using a meter stick, ruler, or measuring tape -Use the Pythagorean Theorem to test if the corner is a right-angle or not!