lesson 57 pyth. theorem.notebook January 08, 2016 Warm Up ~ Identify the blue line drawn in the triangle. 1) ________ 4) ________ 2) ________ 3) ________ 5) ________ lesson 57 pyth. theorem.notebook January 08, 2016 Midsegment Theorem. A midsegment is half the length of the side opposite to it and is parallel to that side. 1) Find x. ______ x + 5 yo 2) Find y. ______ 57o 40 lesson 57 pyth. theorem.notebook MP and LP are angle bisectors of ∆LMN. a. Find the distance from P to MN. b. Find the measure of <LMN January 08, 2016 lesson 57 pyth. theorem.notebook January 08, 2016 lesson 57 pyth. theorem.notebook January 08, 2016 What is point B called? If AC=3x+9 and AB=2x, find A B AB=____ BC=____ AC=____ C lesson 57 pyth. theorem.notebook January 08, 2016 lesson 57 pyth. theorem.notebook January 08, 2016 lesson 57 pyth. theorem.notebook January 08, 2016 lesson 57 pyth. theorem.notebook January 08, 2016 lesson 57 pyth. theorem.notebook January 08, 2016 lesson 57 pyth. theorem.notebook Turn in Homework. Get ready for the 5.15.4 Quiz January 08, 2016 lesson 57 pyth. theorem.notebook January 08, 2016 lesson 57 pyth. theorem.notebook January 08, 2016 lesson 57 pyth. theorem.notebook January 08, 2016 lesson 57 pyth. theorem.notebook January 08, 2016 lesson 57 pyth. theorem.notebook 1. Write the angles in order from smallest to largest. January 08, 2016 5.5/5.6 review 2. Write the sides in order from shortest to longest. 3. The lengths of two sides of a triangle are 17 cm and 12 cm. Find the range of possible lengths for the third side. 4. Compare m∠ABC and m∠DEF. lesson 57 pyth. theorem.notebook January 08, 2016 5) Using the hinge theorem and basic geometry concept, what is the range of values for x. 15 30o 28o X+2 4) If 2 sides of a triangle are 16 and 20, write the range of values the 3rd side can. Write is simplest radical form: 1) 2) 3) Warm UP lesson 57 pyth. theorem.notebook January 08, 2016 GOAL 1) Use the Pythagorean Theorem and its converse to solve problems. 2) Use Pythagorean inequalities to classify triangles. Theorems (2) Conv. Pythagorean Th. Pyth. Inequality Th. Definitions (1) Pythagorean triple lesson 57 pyth. theorem.notebook Before we begin, let's review simplifying radicals. January 08, 2016 lesson 57 pyth. theorem.notebook January 08, 2016 a2 + b2 = c2 The Pythagorean Theorem is probably the most famous mathematical relationship. As you learned in Lesson 16, it states that in a right triangle, the sum of the squares of the lengths of the legs equals the square of the length of the hypotenuse. lesson 57 pyth. theorem.notebook January 08, 2016 Using the Pythagorean Theorem Find the value of x. Give your answer in simplest radical form. lesson 57 pyth. theorem.notebook January 08, 2016 Randy is building a rectangular picture frame. He wants the ratio of the length to the width to be 3:1 and the diagonal to be 12 centimeters. How wide should the frame be? Round to the nearest tenth of a centimeter. lesson 57 pyth. theorem.notebook January 08, 2016 What if...? According to the recommended safety ratio of all ladders to be placed at a ratio of 4:1, how high will a 30foot ladder reach when placed against a wall? Round to the nearest inch. Building lesson 57 pyth. theorem.notebook January 08, 2016 A set of three nonzero whole numbers a, b, and c such that a2 + b2 = c2 is called a Pythagorean triple. lesson 57 pyth. theorem.notebook January 08, 2016 Identifying Pythagorean Triples Find the missing side length. Tell if the side lengths form a Pythagorean triple. Explain. lesson 57 pyth. theorem.notebook January 08, 2016 The converse of the Pythagorean Theorem gives you a way to tell if a triangle is a right triangle when you know the side lengths. lesson 57 pyth. theorem.notebook January 08, 2016 You can also use side lengths to classify a triangle as acute or obtuse. lesson 57 pyth. theorem.notebook January 08, 2016 To understand why the Pythagorean inequalities are true, consider ∆ABC. lesson 57 pyth. theorem.notebook January 08, 2016 Classifying Triangles 1) Can the triangle even exist? 2) If yes, what type of triangle is it? Acute, Obtuse, or Right. 5, 7, 10 5, 8, 17 7, 12, 16 11, 18, 34 3.8, 4.1, 5.2 6, 8, 10 lesson 57 pyth. theorem.notebook Homework! Due next class. 5.7 pg 364 #127 all + Worksheet January 08, 2016 lesson 57 pyth. theorem.notebook January 08, 2016
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