Guided Notes/Practice 1/18: We will learn to apply Pythagorean Theorem to solve for missing side lengths of right triangles. Do Now: Have Out: - Today’s Handouts - HW due today Be a Tri-Angel today Agenda: Do Now! Guided Notes/Practice IP ET Homework Handout (11 problems) 1st Period

We will learn to apply Pythagorean Theorem to solve for missing side lengths of right triangles. Write down objective & begin Do Now!

it has a box (right angle) The values in the chart represent the sides of a right triangle. Complete the chart below. Compare the values of a2 + b2 and c2. Write an algebraic equation to represent this relationship. Describe what the variables in your equation above represent by completing the following phrases: - ∆XYZ is a _____________ triangle because ___________________________________________________________ - a and b represent the _____________ of ∆XYZ because ________________________________________________ - c represents the __________________ of ∆XYZ because ________________________________________________ 9 16 25 25 25 144 169 169 it is opposite the right angle of the triangle .36 .64 1 1 c2 = a2 + b2 right it has a box (right angle) LEGS they form the right angle of the triangle HYPOTENUSE

Pythagorean Theorem: If a triangle is a _____________ triangle, then the square of the longest side (______________) is equal to the ____________of the squares of the other two sides (__________). RIGHT HYPOTENUSE SUM LEGS OR

Example 1a Pythagorean Theorem Substitute. Square. Find the value of x. Write your answer in simplest radical form and as a decimal rounded to nearest hundredth. SOLUTION (hypotenuse)2 = (leg)2 + (leg)2 Pythagorean Theorem 52 = 32 + x2 Substitute. 25= 9 + x2 Square. 16 = x2 Subtract 9 from both sides 4 = x Find the positive square root.

Example 1a Not possible because not a right triangle Find the value of x. Write your answer in simplest radical form and as a decimal rounded to nearest hundredth. SOLUTION Not possible because not a right triangle

Example 1c Pythagorean Theorem Substitute. Square. Add. Find the value of x. Write your answer in simplest radical form and as a decimal rounded to nearest hundredth.   2 SOLUTION (hypotenuse)2 = (leg)2 + (leg)2 Pythagorean Theorem   Substitute. x2 = 4 + 12 Square. x2 = 16 Add. x = 4 Find the positive square root.

Example 1c Maritza and Melanie run 8 miles north and then 5 miles west. What is the shortest distance, to the nearest hundredth of a mile, they must travel to return to their starting point?

EXAMPLE 4 SOLUTION = + 162 = 42 + x2

EXAMPLE 3 Substitute. Square. Subtract 16 from each side. Standardized Test Practice SOLUTION 162 = 42 + x2 Substitute. 256 = 16 + x2 Square. 240 = x2 Subtract 16 from each side. 240 = x Find positive square root. 15.491 ≈ x Approximate with a calculator. ANSWER The ladder is resting against the house at about 15.5 feet above the ground. The correct answer is D.

Example 4 Pythagorean Theorem Substitute. Square Add.   SOLUTION (hypotenuse)2 ? (leg)2 + (leg)2 Pythagorean Theorem   Substitute. 64 ?16 + 48 Square 64 ?64 Add. 64 = 64 YES, these side lengths make a right triangle!

Pythagorean Triples: Any set of _____ ____________ numbers {a, b, c} that satisfies _______________. IF it satisfies the rule stated above, then the three numbers create a _______ ____________. three whole c2 = a2 + b2 right triangle Example 5: Determine if the following sets of numbers are Pythagorean Triples. Justify your response.    

Example 5: Determine if the following sets of numbers are Pythagorean Triples. Justify your response. b. {7, 9, 8} c. {37, 12, 35} c2 ? a2 + b2 c2 ? a2 + b2 372 ? 122 + 352 92 ? 72 + 82 81 ? 49 + 64 1369 ? 144 + 1225 1369 = 1369 81 < 113 Since c2 < a2 + b2 then this set of numbers is NOT a Pythagorean Triple Since c2 = a2 + b2 then this set of numbers is a Pythagorean Triple