19.2 Pythagorean Theorem.

Slides:

Advertisements

Similar presentations

Special Right Triangles

Advertisements

Special Right Triangles

Two Special Right Triangles

Special Right Triangles Moody Mathematics. Take a square… Moody Mathematics.

Right Triangle Trigonometry

Pythagorean Theorem Properties of Special Right Triangles

Measurement Pythagorean Relationship 3 (Finding the length of an unknown leg)

Pythagorean Relationship 2 (Finding the length of the Hypotenuse)

Special Right Triangles

Unit 2 - Right Triangles and Trigonometry

Special Shortcuts for and Triangles

Special Shortcuts for and Triangles

CH 8 Right Triangles. Geometric Mean of 2 #’s If you are given two numbers a and b you can find the geometric mean. a # = # b 3 x = x 27 Ex ) 3 and 27.

Two Special Right Triangles

UNIT QUESTION: What patterns can I find in right triangles?

Special Right Triangles

Special Right Triangles

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.

Lesson 56: Special Right Triangles

Geometry Section 9.4 Special Right Triangle Formulas

The Distance and Midpoint Formulas and Other Applications 10.7.

Bell Ringer Get out your 10.5/10.7 homework assignment and formula sheet Get out your notebook and prepare to take notes on Section 11.2 What do you know.

MA.912.G.5.1 : Apply the Pythagorean Theorem and its Converse. A.5 ft B.10 ft C. 15 ft D. 18 ft What is the value of x? x 25 ft 20 ft.

Ch 9.1 The Pythagorean Theorem Definition of the Day Right Triangle Legs of a Triangle Hypotenuse of a Triangle The Pythagorean Theorem.

Right Triangles And the Pythagorean Theorem. Legs of a Right Triangle Leg -the two sides of a right triangle that form the right angle Leg.

Special Right Triangles

W ARM -U P  Name the type of angle by the degree measure.  1.78 o o  o 4.13 o.

4.5 Isosceles and Equilateral Triangles. Isosceles Triangles At least two sides are of equal length. It also has two congruent angles. Base Angles Base.

1 Isosceles and Equilateral Triangles. 2 Parts of an Isosceles Triangle An isosceles triangle is a triangle with two congruent sides. The congruent sides.

30°, 60°, and 90° - Special Rule The hypotenuse is always twice as long as the side opposite the 30° angle. 30° 60° a b c C = 2a.

Objective The student will be able to:

Special Right Triangles. Draw 5 squares with each side length increasing by

Special Right Triangles

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; Objective: To find the perimeter and area of a triangle.

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

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.

11.2 Pythagorean Theorem. Applies to Right Triangles Only! leg Leg a hypotenuse c Leg b.

Objective - To find missing sides of right triangles using the Pythagorean Theorem. Applies to Right Triangles Only! hypotenuse c leg a b leg.

Special Right Triangles

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

Honors Geometry Section 5.5 Special Right Triangle Formulas.

Triangle Congruence 4.5 Isosceles and Equilateral Triangles.

Exploring. Pythagorean Theorem For any right triangle, the area of the square on the hypotenuse is equal to the sum of the areas of the squares on 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.

Classifying Triangles How many degrees can be found in all triangles? 180 We can classify triangles 2 ways: By their angles By their sides.

7.1 – Apply the Pythagorean Theorem. Pythagorean Theorem: leg hypotenuse a b c c 2 = a 2 + b 2 (hypotenuse) 2 = (leg) 2 + (leg) 2 If a triangle is a right.

Objective The learner will solve problems using the Pythagorean Theorem.

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.

The Pythagorean Theorem

SOL 8.10 Pythagorean Theorem.

Objective The student will be able to:

11.2 Pythagorean Theorem.

12-2 The Pythagorean Theorem

Objective - To find missing sides of right triangles using the Pythagorean Theorem. Applies to Right Triangles Only! hypotenuse c leg a b leg.

6-3 The Pythagorean Theorem Pythagorean Theorem.

5.7: THE PYTHAGOREAN THEOREM (REVIEW) AND DISTANCE FORMULA

5-3: The Pythagorean Theorem

The Isosceles Triangle Theorems

7.4 Special Right Triangles f g u i l b e r t.

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.

5.1 Special Right Triangles

The Pythagorean Theorem

10-1 The Pythagorean Theorem

Presentation transcript:

19.2 Pythagorean Theorem

A right triangle is a triangle that has a right (90 degree) angle A right triangle is a triangle that has a right (90 degree) angle. The 2 sides that form the right angle are called the legs of the triangle and the side opposite the right angle is called the hypotenuse. hypotenuse leg leg leg hypotenuse leg

The Pythagorean Theorem relates the sides of any right triangle The Pythagorean Theorem relates the sides of any right triangle. If a and b represent the legs and c the hypotenuse, then

Find the length of the hypotenuse: c 24 dm 10 dm

Find the length of the hypotenuse: 8.00 cm 3.90 cm c

Find the length of the missing side b

Find the length of the missing side b

Use the Pythagorean theorem. How long must a guy wire be to reach from the top of a 15-m telephone pole to a point on the ground 10 m from the foot of the pole? Use the Pythagorean theorem. 10 m 15 m c

There are two special right triangles that we will further explore There are two special right triangles that we will further explore. They are called a 45, 45, 90 right triangle and a 30, 60 ,90 right triangle. The numbers refer to the measure of the angles in degrees.

The 45, 45, 90 triangle is an isosceles triangle which means the two legs have equal measure. hypotenuse Since the legs are equal, by the Pyth.Theorem, the hypotenuse has length = leg

Find the hypotenuse of an isosceles triangle that has equal sides of 2 m. ? Hypotenuse has length =

If the hypotenuse of a 45, 45, 90 triangle is 5 cm long, how long is each leg. ? 5 cm Since hyp = leg

An equilateral triangle has 3 equal sides and 3 equal angles that each measures 60 degrees. The height bisects both the angle and opposite side making a 30, 60, 90 triangle. 30 ½ side or ½ hypot 60 60

Applying the Pythagorean Th Applying the Pythagorean Th. to this 30, 60, 90 triangles gives the following relations: 30 2x, side opposite right angle or longest side other leg 60 x, side opposite 30 or short leg

Find the missing measures. 30 Hyp. = 2(short leg) = 2(7 in) = 14 in Other leg = short leg ? ? 60 7 in

Find the missing measures. 60 ? Other leg = short leg ? 30 8 cm Hyp. = 2(short leg) = 2( 4.6in) = 9.2 in