Matematika The mathematic is difficult and fearfull I hope you can learn mathematics.

Slides:

Advertisements

Similar presentations

Advertisements

Square Numbers To SQUARE a number means to multiply it by itself For example the square of 7 is 7  7 = 49 We shorten this to 7 2 = 7  7 = 49 We read.

Honors Geometry Section 5.4 The Pythagorean Theorem

Copyright © Ed2Net Learning, Inc. 11 Grade 8 Pythagorean Theorem #1.

Pythagorean Theorem Please view this tutorial and answer the follow-up questions on loose leaf to turn in to your teacher.

Section 11-2 The Pythagorean Theorem SPI 32A: apply the Pythagorean Theorem to real life problem illustrated by a diagram Objectives: Solve problems using.

CONFIDENTIAL 1 Grade 8 Pre-Algebra Pythagorean Theorem 2.

Section 8-2 The Pythagorean Theorem Objectives: Solve problems using the Pythagorean Theorem Right Angle: angle that forms 90° Hypotenuse: in a right triangle,

Geometry Section 9.4 Special Right Triangle Formulas

Aim: How do we find the lengths of the sides in a right triangle? Do Now 1. Solve 2(x + 5) = Find the measure of the missing angle? 48 o 17 o 100.

Chapter 7.1 & 7.2 Notes: The Pythagorean Theorem and its Converse

Lesson 10-2 Warm-Up.

9/23/ : The Pythagoream Theorem 5.4: The Pythagorean Theorem Expectation: G1.2.3: Know a proof of the Pythagorean Theorem and use the Pythagorean.

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.

Do Now 5/16/11 Copy HW in your planner. Copy HW in your planner. Text p. 467, #8-30 evens, & 19 Text p. 467, #8-30 evens, & 19 Be ready to copy POTW #6.

Copyright © Cengage Learning. All rights reserved. CHAPTER The Six Trigonometric Functions The Six Trigonometric Functions 1.

Lesson #6: Triangles & Pythagorean Theorem

Step 1: Square Longest side Step 2: Add Step 3: Square Root Step 1: Square Shorter side Step 2: Subtract Step 3: Square Root 7cm 9cm x 4cm 8cm x 12cm 7cm.

The Pythagorean Relationship. In words The Pythagorean Relationship states that in a right angle triangle, the square of the hypotenuse is equal to the.

Classifying Triangles By Angles Acute: all three angles are less than 90 ◦ Obtuse: one angle is greater than 90 ◦ Right: one angle measure is 90 ◦ By.

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

Lesson 9.4 Geometry’s Most Elegant Theorem Objective: After studying this section, you will be able to use the Pythagorean Theorem and its converse.

GHSGT Review Triangles and Circles.

- Special Right Triangles Chapter 4 Understanding Trigonometric Functions Language Objectives: We will review Special Right Triangles by do worksheet 11A.

PYTHAGORAS Aim: To be able to know Pythagoras’ Theorem All: Will be able to recall theorem. Most: Will be able to use to find the length of hypotenuse.

Sullivan Algebra and Trigonometry: Section R.3 Geometry Review Objectives of this Section Use the Pythagorean Theorem and Its Converse Know Geometry Formulas.

College Algebra Section R.3 Geometry Review Objectives of this Section Use the Pythagorean Theorem and Its Converse Know Geometry Formulas.

14 Chapter Area, Pythagorean Theorem, and Volume

Starter Write down a definition of the hypotenuse

1 An isosceles triangle has one line of symmetry.

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.

 Only works in right angled triangles  Nothing to do with angles.

Trigonometry – Right Angled Triangles By the end of this lesson you will be able to identify and calculate the following: 1. Who was Pythagoras 2. What.

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

Jeopardy Pythag. Thm. Pythag. Thm. Apps Simplifying Radicals Inequalities Family Tree Of Numbers Q $100 Q $200 Q $300 Q $400 Q $500 Q $100 Q $200 Q $300.

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.

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

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

Trigonometry – Right Angled Triangles By the end of this lesson you will be able to identify and calculate the following: 1. Find the shorter side length.

Honors Geometry Section 5.5 Special Right Triangle Formulas.

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.

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

Copyright © Cengage Learning. All rights reserved. 12 Geometry.

s.html Year 9 Mathematics Pythagoras Theorem.

Chapter 7 Right Triangles and Trigonometry Objectives: Use calculator to find trigonometric ratios Solve for missing parts of right triangles.

Warm Up For Exercises 1 and 2, find the value of x. Give your answer in simplest radical form Simplify expression. 3.

About 2500 years ago, Greek mathematician named Pythagoras (569 B.C.-500 B.C.) discovered a special relationship between the sides of a right angled.

Geometry/Trig 2 Name __________________________

Sides in a right angled triangle

Section 11-2 The Pythagorean Theorem SPI 32A: apply the Pythagorean Theorem to real life problem illustrated by a diagram Objectives: Solve problems.

a right-angled triangle

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

Objectives Use the Pythagorean Theorem and its converse to solve problems. Use Pythagorean inequalities to classify triangles.

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

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

Pythagorean Theorem What is it??

Pythagorean Theorem.

Pythagorean Theorem.

MULTIMEDIA LESSON PLAN ON PYTHAGORAS THEOREM

Pythagorean Theorem.

Using Pythagoras’ Theorem

Solve for the unknown side or angle x

Pythagorean Theorem OR.

Additional Topics in Math Lessons 1-2

Pythagoras’ Theorem.

Pythagorean Theorem.

The Pythagorean Theorem a2 + b2 = c2

Presentation transcript:

Matematika The mathematic is difficult and fearfull I hope you can learn mathematics

PYTHAGOREAN THEOREM CLASS : VIII SEMESTER : 1 B Y SULISTYANA, S.Pd. SMP 1 WONOSARI GK LANJUT

REMEMBER Triangles can be classified according to the length of their sides. They can be classified as either equilateral, isosceles or scalene.

Triangles can be classified by their angles as well. A triangle with one right angle is said to be a right triangle. Right triangle

In any triangle, the longest side is opposite the largest angle; so in a right triangle, the longest side is opposite the right angle. This side has a special name. It is called the hypotenuse.

Pythagorean Theorem In any right angled triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. The rule is written as c 2 = a 2 + b 2 where a and b are the two shorter sides and c is the hypotenuse. The hypotenuse is the longest side of a right-angled triangle and is always the side that is opposite the right angle.

We are able to find the length of the hypotenuse when we are given the length of the two shorter sides by substituting into the formula c 2 = a 2 + b 2 Finding the hypotenuse

Solving

Finding a shorter side Sometimes a question will give you the length of the hypotenuse and ask you to find one of the shorter sides. In such examples, we need to rearrange Pythagoras’ formula. Given that c 2 = a 2 + b 2, we can rewrite this as: a 2 = c 2 - b 2 or b 2 = c 2 + a 2.

exercise

2. The diagonal of the rectangular sign at right is 34 cm. If the height of this sign is 25 cm, find the width. 3 The diagonal of a rectangle is 120 cm. One side has a length of 70 cm. Find: a the length of the other side b the perimeter of the rectangle c the area of the rectangle. 4 An equilateral triangle has sides of length 20 cm. Find the height of the triangle. 5 The road sign shown at left is in the form of an equilateral triangle. Find the height of the sign and, hence, find its area. 6 A ladder that is 7 meter long leans up against a vertical wall. The top of the ladder reaches 6.5 m up the wall. How far from the wall is the foot of the ladder? 7 A tent pole that is 1.5 m high is to be supported by ropes attached to the top. Each rope is 2 m long. How far from the base of the pole can each rope be pegged?