Section 10.2 Triangles Triangle: A closed geometric figure that has three sides, all of which lie on a flat surface or plane. Closed geometric figures.

Slides:

Advertisements

Similar presentations

The Pythagorean Theorem leg hypotenuse leg Applies to Right Triangles only! The side opposite the right angle The sides creating the right angle are called.

Advertisements

Geometry Agenda 1. ENTRANCE 2. Go over Tests/Spiral

The Pythagorean Theorem. The Right Triangle A right triangle is a triangle that contains one right angle. A right angle is 90 o Right Angle.

Lesson 10.1 The Pythagorean Theorem. The side opposite the right angle is called the hypotenuse. The other two sides are called legs. We use ‘a’ and ‘b’

Pythagorean Theorem By: Tytionna Williams.

4.4: THE PYTHAGOREAN THEOREM AND DISTANCE FORMULA

8-1 The Pythagorean Theorem and Its Converse. Parts of a Right Triangle In a right triangle, the side opposite the right angle is called the hypotenuse.

Benchmark 40 I can find the missing side of a right triangle using the Pythagorean Theorem.

The Pythagorean Theorem

Section 11.6 Pythagorean Theorem. Pythagorean Theorem: In any right triangle, the square of the length of the hypotenuse equals the sum of the squares.

Algebra 12.5 The Pythagorean Theorem. Radical Review  Simplify each expression. You try! = 5 = 8/3 = 28 = 9/5.

+ Warm Up B. + Homework page 4 in packet + #10 1. Given 2. Theorem Given 4. Corresponding angles are congruent 5. Reflexive 6. AA Similarity 7.

Section 3-5 p. 137 Goal – to solve problems using the Pythagorean Theorem.

Pythagorean Theorum Adham Jad. What is a triangle? How many sides does a triangle have? What is the sum of angles in a triangle? Background & Concept.

11-3: The Pythagorean Theorem Pg.546. Objective & Vocabulary 1.Find the length of a side of a right triangle. Hypotenuse (pg.546): in a right triangle,

© 2008 Pearson Addison-Wesley. All rights reserved Chapter 1 Section 9-4 The Geometry of Triangles: Congruence, Similarity, and the Pythagorean Theorem.

Objective The student will be able to:

Learning Outcome: Discover a relationship among the side lengths of a right triangle.

Triangles and Lines – Special Right Triangles There are two special right triangles : 30 – 60 – 90 degree right triangle 45 – 45 – 90 degree right triangle.

© 2010 Pearson Prentice Hall. All rights reserved. CHAPTER 10 Geometry.

Right Triangles and Trigonometry Chapter Geometric Mean  Geometric mean: Ex: Find the geometric mean between 5 and 45 Ex: Find the geometric mean.

Pythagorean Theorem Unit 7 Part 1. The Pythagorean Theorem The sum of the squares of the legs of a right triangle is equal to the square of the hypotenuse.

Chapter 1: Square Roots and the Pythagorean Theorem Unit Review.

The Pythagorean Theorem

Topic 10 – Lesson 9-1 and 9-2. Objectives Define and identify hypotenuse and leg in a right triangle Determine the length of one leg of a right triangle.

OBJECTIVE I will use the Pythagorean Theorem to find missing sides lengths of a RIGHT triangle.

I can use proportions to find missing lengths in similar figures.

Pythagorean Theorem - Thurs, Oct 7

11.4 Pythagorean Theorem Definitions Pythagorean Theorem

Similar Triangles and Pythagorean Theorem Section 6.4.

A c b Created by ﺠﻴﻄ for mathlabsky.wordpress.com.

RIGHT TRIANGLES A RIGHT TRIANGLE is a triangle with one right angle. a b c Sides a and b are called legs. Side c is called the hypotenuse.

The Pythagorean Theorem Use the Pythagorean Theorem to find the missing measure in a right triangle including those from contextual situations.

The Pythagorean Theorem The Ladder Problem. Right Triangles Longest side is the hypotenuse, side c (opposite the 90 o angle) The other two sides are the.

Pythagorean Theorem and Special Right Triangles. Anatomy of a Right Triangle Why is a right triangle called a right triangle? Because it is a triangle.

Pythagorean Theorem & Distance Formula Anatomy of a right triangle The hypotenuse of a right triangle is the longest side. It is opposite the right angle.

10-1 The Pythagorean Theorem. LEGS Hypotenuse Problem 1: Finding the Length of a Hypotenuse The tiles shown below are squares with 6-in. sides. What.

Refresh Your Skills for Chapter 12.  If you split an equilateral triangle in half along an altitude, you create two right triangles with angles of 30°,

Section 8-1. Find the geometric mean between each pair of numbers. 4 and 9.

Pythagorean Theorem. What is a right triangle? It is a triangle which has an angle that is 90 degrees. The two sides that make up the right angle are.

 Right Triangle – A triangle with one right angle.  Hypotenuse – Side opposite the right angle and longest side of a right triangle.  Leg – Either.

Section 10.2 Triangles Math in Our World. Learning Objectives  Identify types of triangles.  Find one missing angle in a triangle.  Use the Pythagorean.

I can find missing lengths in similar figures and use similar figures when measuring indirectly.

The Pythagorean Theorem

Pythagorean Theorem and it’s Converse

The Right Triangle and The Pythagorean Theorem

Rules of Pythagoras All Triangles:

Objective The student will be able to:

The Pythagorean Theorem

12-2 The Pythagorean Theorem

Pythagorean Theorem.

Math 3-4: The Pythagorean Theorem

5.4: The Pythagorean Theorem

8-2 The Pythagorean Theorem and Its Converse

5-7 The Pythagorean Theorem

5.7: THE PYTHAGOREAN THEOREM (REVIEW) AND DISTANCE FORMULA

5-3: The Pythagorean Theorem

Similar Figures.

Pythagorean Theorem a²+ b²=c².

Right Triangles Unit 4 Vocabulary.

6.5 Pythagorean Theorem.

5.4: The Pythagorean Theorem

If a triangle is a RIGHT TRIANGLE, then a2 + b2 = c2.

Similar Triangles Review

Pythagoras’ Theorem.

Geometric Mean and the Pythagorean Theorem

The Pythagorean Theorem

10-1 The Pythagorean Theorem

1-6: Midpoint and Distance

Presentation transcript:

Section 10.2 Triangles Triangle: A closed geometric figure that has three sides, all of which lie on a flat surface or plane. Closed geometric figures If you start at any point and trace along the sides, you end up at the starting point.

The sum of the measures of the three angles of any triangle is 180º.

Example 1 Find the measure of angle A for the triangle ABC. Solution: mA + mB + mC =180º mA + 120º + 17º = 180º mA + 137º = 180º mA = 180º − 137º = 43º

Example 2 Find the measures of angles 1 through 5.

Triangles and Their Characteristics

Similar Triangles Similar figures have the same shape, but not necessarily the same size. In similar triangles, the angles are equal but the sides may or may not be the same length. Corresponding angles are angles that have the same measure in the two triangles. Corresponding sides are the sides opposite the corresponding angles.

Example 3 Find the missing length x. Solution: Because the triangles are similar, their corresponding sides are proportional:

Example: Using Similar Triangles Find the missing length x. The missing length of x is 11.2 inches.

RIGHT TRIANGLE In a right triangle, the side opposite the right angle is called the hypotenuse; it is the longest side in the right triangle. The other two sides are the legs of the triangle.

PYTHAGOREAN THEOREM In any right triangle, the square of the length of the hypotenuse equals the sum of the squares of the lengths of the other two sides:

Example: Using the Pythagorean Theorem Find the length of the hypotenuse c in this right triangle: Let a = 9 and b = 12 C

Example: Using the Pythagorean Theorem Find the length a in the right triangle below. 39 a Solution: 36