c2 = a2 + b2 Pythagoras's Theorem c a b In any right angled triangle,

Slides:

Advertisements

Similar presentations

Pythagoras Bingo. Pick 8 from the list C no 16124yes Pythagorean triple Hypotenuse Pythagoras theorem.

Advertisements

Test For Congruent Triangles. Test 1 3 cm 4 cm 3 cm Given three sides : SSS Two triangles are congruent if the three sides of one triangle are equal to.

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.

Squaring a Number To square a number means to :

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’

There are three ratios that you need to learn: Where are the hypotenuse, adjacent and opposite lengths. This is opposite the right-angle This is next to.

Geometry Section 9.4 Special Right Triangle Formulas

5.1 Special Right Triangles. What you should already know… Right triangles have one 90 o angle The longest side is called the HYPOTENUSE  It is directly.

The Pythagorean Theorem

Presented By: Alexander Sarkissian. Pythagoras’s Theorem  First we will start with the common right triangle.  Side a= Adjacent side  Side b= Opposite.

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

AREA OF A TRIANGLE. Given two sides and an included angle:

4-6 Congruence in Right Triangles M.11.C B

4.6 Congruence in Right Triangles In a right triangle: – The side opposite the right angle is called the hypotenuse. It is the longest side of the triangle.

8.2 Special Right Triangles. Side lengths of Special Right Triangles Right triangles whose angle measures are 45°-45°-90° or 30°- 60°-90° are called special.

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

Pythagorean Theorem Chapter 3 – 5. What’s a, b, & c? a & b are the two sides that form the 90° angle a & b are also known as “legs” of a right triangle.

Bell Ringer 30  60  3 X Y Find x and y. Objective I can evaluate the legs and hypotenuse of a triangle in word problems.

1 Trig. Day 3 Special Right Triangles. 2 45°-45°-90° Special Right Triangle 45° Hypotenuse X X X Leg Example: 45° 5 cm.

4.4 Pythagorean Theorem and the Distance Formula Textbook pg 192.

Pythagoras' Theorem © Victoria Smith Begin. Right Angled Triangles Pythagoras’ Theorum will only work on a right angled triangle. ac b The longest side,

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.

Pythagoras c² a² b² c a b c² = a² + b² has the same area as the two smaller squares added together. The large square + PYTHAGORAS THEOREM is applied to.

 Remember the pattern for right triangles: Area of small square + Area of medium square = Area of large square.

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.

What is a right triangle? A triangle with a right angle.

Right Triangle Naming Conventions. When we studied Pythagorean Theorem: a b c.

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

5.1 Special Right Triangles

Special Right Triangles

The Distance and Midpoint Formulas

8-2 Special Right triangles

hypotenuse opposite adjacent Remember

Midpoint And Distance in the Coordinate Plane

5.1 Special Right Triangles

12-2 The Pythagorean Theorem

Pythagoras’ Theorem and Trigonometry

Using the Pythagoras Theorem.

Starter Jane is 40. Chris is 10. Chris is ¼ of Jane’s age.

Subject knowledge, what is it good for?

8-2 Special Right Triangles

Theorem The area A of a triangle is

Hyp Opp Adj c a b c 2 = a 2 + b 2 b 2 = c 2 - a 2 a 2 = c 2 - b 2 xo

5.7: THE PYTHAGOREAN THEOREM (REVIEW) AND DISTANCE FORMULA

45°-45°-90° Special Right Triangle

Page 134 First, some definitions.

Pythagoras' Theorem.

6.5 Pythagorean Theorem.

Special Right Triangles

Special Right Triangles

©G Dear 2009 – Not to be sold/Free to use

Geometric Reasoning.

Pythagoras’ Theorem.

Finding the hypotenuse

5.1 Special Right Triangles

Special Right Triangles

The Pythagorean Theorem

Special Right Triangles

In a right triangle, the side opposite the right angle is called the hypotenuse. This side is always the longest side of a right triangle. The other.

10-1 The Pythagorean Theorem

Special Right Triangles

Maths Unit 23 – Pythagoras & Trigonometry

The Pythagorean Theorem a2 + b2 = c2

Presentation transcript:

c2 = a2 + b2 Pythagoras's Theorem c a b In any right angled triangle, Label the longest side (the hypotenuse) as c. Label the two other (shorter) sides as a and b. Then…….. b a c c2 = a2 + b2

a2 = c2 - b2 Pythagoras's Theorem c a b If you wanted one of the two shorter sides, then You can rearrange the formula…… b a c a2 = c2 - b2

x = 10 cm x 6cm 8cm Example 1… Find x As we are finding the hypotenuse, then use the version of the formula with the + sign. 8cm 6cm x c2 = a2 + b2 x2 = 62 + 82 x2 = 36 + 64 x2 = 100 x = 100 x = 10 cm

Example 2… Find x As we are finding a shorter side, then use the version of the formula with the - sign. 12cm x 17cm a2 = c2 - b2 x2 = 172 - 122 x2 = 289 - 144 x2 = 145 x = 145 x = 12.1 cm