lesson 5-7 pyth. theorem.notebook

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