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

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

Special Right Triangles Chapter 7.4. Special Right Triangles triangles triangles.

Special Right Triangles Keystone Geometry

Special Right Triangles

EXAMPLE 4 SOLUTION Method 1: Use a Pythagorean triple. A common Pythagorean triple is 5, 12, 13. Notice that if you multiply the lengths of the legs of.

EXAMPLE 4 Find the length of a hypotenuse using two methods SOLUTION Find the length of the hypotenuse of the right triangle. Method 1: Use a Pythagorean.

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.

SPECIAL RIGHT TRIANGLES. A special right triangle is a right triangle with some features that make calculations on the triangle easier. WHAT ARE SPECIAL.

Families 30 60, 90 45, 90 Resource Geometry/ Sophomores.

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.

Unit 7 Part 2 Special Right Triangles 30°, 60,° 90° ∆s 45°, 45,° 90° ∆s.

Geometry Section 9.4 Special Right Triangle Formulas

The Pythagorean Theorem Converse & Triangle Inequality Theorem  Pythagoras, circa 570 BC.

Pythagorean Theorem Mr. Parks Algebra Support. Objective The student will be able to: Find the missing side of a right Triangle using the Pythagorean.

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

Pythagorean Theorem Use the Pythagorean Theorem to find the missing length of the right triangle. 1.

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.

Warm Up For Exercises 1 and 2, find the value of x. Give your answer in simplest radical form

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.

Geometry 4.4 SWLT: Use the Pythagorean Theorem to find side lengths of Right Triangles.

Objective The student will be able to:

Created by Jeremy Hamilton The Pythagorean therom will only work on right triangles because a right triangle is the only triangle with a hypotenuse and.

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

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

Special Right Triangles What kind of triangle is this? Isosceles What are the measures of the other two angles? 45° and 45°

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.

4.7 Triangle Inequalities. Theorem 4.10 If one side of a triangle is longer than another side, then the angle opposite the longer side is larger than.

Pythagorean Theorem What is it and how does it work? a 2 + b 2 = c 2.

Special Right Triangles Keystone Geometry

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

 It is the way you find the area of an triangle.  It has three sides.  A. one of the three sides also called a leg  B. one of the three sides also.

Honors Geometry Section 5.5 Special Right Triangle Formulas.

Pythagorean Theorem Converse Special Triangles. Pythagorean Theorem What do you remember? Right Triangles Hypotenuse – longest side Legs – two shorter.

Name:________________________ Date:______________ 1 Chapter 11 Lesson 5 StandardAlgebra 1 standard 2.0 Understand and use the operation of taking a root.

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.

8-6 and 8-7 Square Roots, Irrational Numbers, and Pythagorean Theorem.

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.

Special Right Triangles. What are Special Right Triangles? There are 2 types of Right triangles that are considered special. We will talk about only one.

Lesson 35: Special Right Triangles and the Pythagorean Theorem

8.1 Pythagorean Theorem and Its Converse

Solving sides of special right triangles

The Distance and Midpoint Formulas

Objective The student will be able to:

8-2 Special Right triangles

12-2 The Pythagorean Theorem

8-2 Special Right Triangles

Pythagorean Theorem.

11.4 Pythagorean Theorem.

Pythagorean Theorem What is it??

Objective The student will be able to:

6.2: Pythagorean Theorem Objectives:

5.4: The Pythagorean Theorem

5.7: THE PYTHAGOREAN THEOREM (REVIEW) AND DISTANCE FORMULA

5-3: The Pythagorean Theorem

7.0: Pythagorean Theorem Objectives:

Pythagorean Theorem a²+ b²=c².

Special Right Triangles Keystone Geometry

Right Triangles Unit 4 Vocabulary.

G3.2 Pythagorean Theorem Objectives:

right triangles Some right triangles are used so frequently that it is helpful to remember some of their properties. These triangles are called.

6.5 Pythagorean Theorem.

Pythagorean Theorem What is it and how does it work? a2 + b2 = c2.

Special Right Triangles

The Pythagorean Theorem

Creating Triangles Concept 41.

10-1 The Pythagorean Theorem

Lesson 3-2 Isosceles Triangles.

Presentation transcript:

Triangles and Lines – Special Right Triangles There are two special right triangles : 30 – 60 – 90 degree right triangle 45 – 45 – 90 degree 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 In a 30 – 60 – 90 right triangle, the hypotenuse is two times longer than the shortest leg x 2x

Triangles and Lines – Special Right Triangles There are two special right triangles : 30 – 60 – 90 degree right triangle 45 – 45 – 90 degree right triangle In a 30 – 60 – 90 right triangle, the hypotenuse is two times longer than the shortest leg Using the Pythagorean theorem, we find the third side is square root of three times bigger than the shortest side. x 2x

Triangles and Lines – Special Right Triangles There are two special right triangles : 30 – 60 – 90 degree right triangle 45 – 45 – 90 degree right triangle Example # 1 : Find the other two sides if the hypotenuse = 10 x 2x =10 In a 30 – 60 – 90 right triangle, the hypotenuse is two times longer than the shortest leg Using the Pythagorean theorem, we find the third side is square root of three times bigger than the shortest side.

Triangles and Lines – Special Right Triangles There are two special right triangles : 30 – 60 – 90 degree right triangle 45 – 45 – 90 degree right triangle Example # 1 : Find the other two sides if the hypotenuse = 10 x = 5 In a 30 – 60 – 90 right triangle, the hypotenuse is two times longer than the shortest leg Using the Pythagorean theorem, we find the third side is square root of three times bigger than the shortest side. 2x =10

Triangles and Lines – Special Right Triangles There are two special right triangles : 30 – 60 – 90 degree right triangle 45 – 45 – 90 degree right triangle Example # 1 : Find the other two sides if the hypotenuse = 10 x = 5 2x =10 In a 30 – 60 – 90 right triangle, the hypotenuse is two times longer than the shortest leg Using the Pythagorean theorem, we find the third side is square root of three times bigger than the shortest side.

Triangles and Lines – Special Right Triangles There are two special right triangles : 30 – 60 – 90 degree right triangle 45 – 45 – 90 degree right triangle Example # 2 : Find the other two sides if the shortest side = 8 x = 8 2x In a 30 – 60 – 90 right triangle, the hypotenuse is two times longer than the shortest leg Using the Pythagorean theorem, we find the third side is square root of three times bigger than the shortest side.

Triangles and Lines – Special Right Triangles There are two special right triangles : 30 – 60 – 90 degree right triangle 45 – 45 – 90 degree right triangle Example # 2 : Find the other two sides if the shortest side = 8 x = 8 2x =16 In a 30 – 60 – 90 right triangle, the hypotenuse is two times longer than the shortest leg Using the Pythagorean theorem, we find the third side is square root of three times bigger than the shortest side.

Triangles and Lines – Special Right Triangles There are two special right triangles : 30 – 60 – 90 degree right triangle 45 – 45 – 90 degree right triangle Example # 2 : Find the other two sides if the shortest side = 8 x = 8 2x =16 In a 30 – 60 – 90 right triangle, the hypotenuse is two times longer than the shortest leg Using the Pythagorean theorem, we find the third side is square root of three times bigger than the shortest side.

Triangles and Lines – Special Right Triangles There are two special right triangles : 30 – 60 – 90 degree right triangle 45 – 45 – 90 degree right triangle Example # 2 : Find the other two sides if the medium length side = x 2x In a 30 – 60 – 90 right triangle, the hypotenuse is two times longer than the shortest leg Using the Pythagorean theorem, we find the third side is square root of three times bigger than the shortest side.

Triangles and Lines – Special Right Triangles There are two special right triangles : 30 – 60 – 90 degree right triangle 45 – 45 – 90 degree right triangle Example # 2 : Find the other two sides if the medium length side = x = 13 2x In a 30 – 60 – 90 right triangle, the hypotenuse is two times longer than the shortest leg Using the Pythagorean theorem, we find the third side is square root of three times bigger than the shortest side.

Triangles and Lines – Special Right Triangles There are two special right triangles : 30 – 60 – 90 degree right triangle 45 – 45 – 90 degree right triangle Example # 2 : Find the other two sides if the medium length side = x = 13 2x = 26 In a 30 – 60 – 90 right triangle, the hypotenuse is two times longer than the shortest leg Using the Pythagorean theorem, we find the third side is square root of three times bigger than the shortest side.

Triangles and Lines – Special Right Triangles There are two special right triangles : 30 – 60 – 90 degree right triangle 45 – 45 – 90 degree right triangle 45 Remember, sides opposite equal angles are congruent. If we let AC and BC = 1 and use Pythagorean theorem… 1 1 A C B ?

Triangles and Lines – Special Right Triangles There are two special right triangles : 30 – 60 – 90 degree right triangle 45 – 45 – 90 degree right triangle 45 Remember, sides opposite equal angles are congruent. If we let AC and BC = 1 and use Pythagorean theorem… 1 1 A C B

Triangles and Lines – Special Right Triangles There are two special right triangles : 30 – 60 – 90 degree right triangle 45 – 45 – 90 degree right triangle 45 The hypotenuse of a 45 – 45 – 90 right triangle is square root two times larger than the equal sides… x x A C B

Triangles and Lines – Special Right Triangles There are two special right triangles : 30 – 60 – 90 degree right triangle 45 – 45 – 90 degree right triangle 45 The hypotenuse of a 45 – 45 – 90 right triangle is square root two times larger than the equal sides… 6 6 A C B Example # 1 : Find the hypotenuse if the congruent sides = 6

Triangles and Lines – Special Right Triangles There are two special right triangles : 30 – 60 – 90 degree right triangle 45 – 45 – 90 degree right triangle 45 The hypotenuse of a 45 – 45 – 90 right triangle is square root two times larger than the equal sides… 6 6 A C B Example # 1 : Find the hypotenuse if the congruent sides = 6

Triangles and Lines – Special Right Triangles There are two special right triangles : 30 – 60 – 90 degree right triangle 45 – 45 – 90 degree right triangle 45 The hypotenuse of a 45 – 45 – 90 right triangle is square root two times larger than the equal sides… x x A C B Example # 2 : Find the congruent sides if the hypotenuse =

Triangles and Lines – Special Right Triangles There are two special right triangles : 30 – 60 – 90 degree right triangle 45 – 45 – 90 degree right triangle 45 The hypotenuse of a 45 – 45 – 90 right triangle is square root two times larger than the equal sides… 15 A C B Example # 2 : Find the congruent sides if the hypotenuse =