Geometry The function of education is to teach one to think intensively and to think critically. Intelligence plus character - that is the goal of true education. Martin Luther King, Jr. Today: Instruction 8.2 Practice

8.2 The Pythagorean Theorem Objectives: 1.Simplify square roots 2.Use the Pythagorean Theorem to find the missing side of a right triangle 3.Classify triangles Vocabulary: Pythagorean Triples

CCSS Content Standards G.SRT.8 Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems. G.MG.3 Apply geometric methods to solve problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios). Mathematical Practices 1 Make sense of problems and persevere in solving them. 4 Model with mathematics.

Then/Now You used the Pythagorean Theorem to develop the Distance Formula. Use the Pythagorean Theorem. Use the Converse of the Pythagorean Theorem.

Find the missing side Identify legs and hypotenuse. 2.Substitute in the Pythagorean equation. 3.Simplify. Helpful Hints:

Pythagorean Triples Three positive integers that satisfy the Pythagorean Theorem equation and therefore form a right triangle

The triangles below appear to be right triangles. Tell whether they are right triangles. Then state if they are Pythagorean Triples. 6 12

9 16 The triangles below appear to be right triangles. Given their side length decide if they actually are: a)possible triangles b)right triangles c)Pythagorean Triples d)None of the These SHOW EVIDENCE!!!!

Concept

Determine whether 10, 11, and 13 can be the measures of the sides of a triangle. If so, classify the triangle as acute, right, or obtuse. Justify your answer.

Indirect Measurement S UPPORT B EAM These skyscrapers are connected by a skywalk with support beams. You can use the Pythagorean Theorem to find the approximate length of each support beam.

Each support beam forms the hypotenuse of a right triangle. The right triangles are congruent, so the support beams are the same length. x 2 = (23.26) 2 + (47.57) 2 Pythagorean Theorem x = (23.26) 2 + (47.57) 2 Find the positive square root. x  Use a calculator to approximate. Indirect Measurement m m xx support beams The length of each support beam is about meters.

Assignment: Pg. 553 #21-29 odd, 38-40, 53 Geometry