Pythagorean Theorem.

Slides:

Advertisements

Similar presentations

The Pythagorean Theorem c a b.

Advertisements

The Pythagorean Theorem Presented by: Tanya Van Dam Kalles Junior High Algebra 2 Spring 2000.

Triangle ABC is an isosceles triangle

Bell Ringer What is the measurement of the missing angles? 65˚ b a cd A triangle sits in between two parallel lines. The sides of the triangle form two.

Exercise Solve x 2 = 4. x = ± 2. Solve x 2 = – 4. no real solution Exercise.

Pythagorean Theorem Formula: a2 + b2 = c2 This formula helps determine two things: the lengths of the different sides of a right triangle, and whether.

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

The Pythagorean Theorem. 8/18/20152 The Pythagorean Theorem “For any right triangle, the sum of the areas of the two small squares is equal to the area.

The Pythagorean Theorem. Pythagoras Lived in southern Italy during the sixth century B.C. Lived in southern Italy during the sixth century B.C. Considered.

Sec 6.6 Pythagorean Theorem. Objective- To solve problems involving the Pythagorean Theorem. For Right Triangles Only! leg hypotenuse - always opposite.

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

Pythagorean Theorem A triangle is a right triangle if and only if the sum of the squares of the lengths of the legs equals the square of the length of.

Geometry Notes Lesson 5.1B Pythagorean Theorem T.2.G.4 Apply the Pythagorean Theorem and its converse in solving practical problems.

Pythagorean Theorem Pre-Algebra ALCOS 7 Lesson Topics Baseball Definitions Pythagorean TheoremPythagorean Theorem Converse of the Pythagorean TheoremConverse.

Pythagoras Lived in southern Italy during the sixth century B.C. Considered the first true mathematician Used mathematics as a means to understand the.

The Pythagorean Theorem. Pythagoras Lived in southern Italy during the sixth century B.C. Considered the first true mathematician Used mathematics as.

The Pythagorean Theorem. Pythagoras Lived in southern Italy during the sixth century B.C. Considered the first true mathematician Used mathematics as.

A b c. Pythagorean Theorem Essential Questions a 2 + b 2 = c 2 The Pythagorean Theorem a 2 + b 2 = c 2 “For any right triangle, the sum of the areas.

Lesson #6: Triangles & Pythagorean Theorem

Course The Pythagorean Theorem OBJECTIVE January 23, 2014 In our study of THE PYTHAGOREAN THEORM (Readiness) the students will be able to Calculate.

Solve the first 4 questions on your worksheet.

By Holly Peters and Adelya Baban

1. Please pick up your SKILL BUILDER. 2. Turn in your Weekend Skill Builder. 3. Start working on the New skill builder now.

8-2 Special Right Triangles. Problem 1: Finding the Length of the Hypotenuse What is the value of each variable?

The Pythagorean Theorem

Bellwork 1.(-8) 2 = √81= = √12= 2√3.

Objectives: 1) To use the Pythagorean Theorem. 2) To use the converse of the Pythagorean Theorem.

1/8/20161 The Pythagorean Theorem Ms.Bianco. 1/8/20162 Pythagoras Lived in southern Italy during the sixth century B.C. Considered the first true mathematician.

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 We are learning to…solve for the missing side of right triangles using the Pythagorean Theorem. Sunday, January 24, 2016.

Bell Ringer What is the measurement of the missing angles? 38˚ b a c d a = 142°, supplementary b = 142°, alternate interior angle c = 38°, corresponding.

The Pythagorean Theorem Presented by: Tanya Van Dam Kalles Junior High Algebra 2 Spring 2000.

Pythagorean Theorem 8/7/07 Pythagorean Theorem DO NOW Construct and define the following triangles: 1.Scalene 2.Isosceles 3.Right 4.Equilateral.

8.2 Pythagorean Theorem and Its Converse Then: You used the Pythagorean Theorem to develop the Distance Formula. Now: 1. Use the Pythagorean Theorem. 2.

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.

The Pythagorean Theorem Pythagoras Lived in southern Italy during the sixth century B.C. Considered the first true mathematician Used mathematics as.

Pythagorean Theorem. Foldable 1.Cut out the rectangle. Fold down the blank to rectangle, and fold up the blank bottom rectangle. Cut only the lines separating.

Sec 6.6 Pythagorean Theorem (Leg1) 2 + (leg2) 2 = (Hyp) 2 hypotenuse Leg 2 Leg 1.

DIRECTIONS SIT IN YOUR DESK AND TURN THEM TO FACE THE POWERPOINT GET A CALCULATOR GET YOUR NOTEBOOK AND WRITING INSTRUMENT OUT TO TAKE NOTES.

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.

Warm Up Write down objective and homework in agenda Lay out homework (none) Homework (Distance & PT worksheet)

Applying Pythagorean Theorem

The Pythagorean Theorem

The Distance and Midpoint Formulas

The Right Triangle and The Pythagorean Theorem

The Pythagorean Theorem

Pythagorean Theorem: Explanation and Application

The Pythagorean Theorem Mr. Clutter VMS Library

LESSON 15 PYTHAGAREAN THEOREM.

Finding the Hypotenuse

The Pythagorean Theorem

The Pythagorean Theorem Mr. Clutter VMS Library

a2 + b2 = c2 Pythagorean Theorem c c b b a a

Pythagorean Theorem What is it??

Pythagorean Theorem.

5.7: THE PYTHAGOREAN THEOREM (REVIEW) AND DISTANCE FORMULA

The Pythagorean Theorem

Pythagorean Theorem Pre-Algebra.

Pythagorean Theorem.

The Pythagorean Theorem

Solve for the unknown side or angle x

The Pythagorean Theorem

Pythagorean Theorem, its Converse and the coordinate system

Applying Pythagorean Theorem

Pythagorean Theorem Pre-Algebra.

Bellwork Find the measure of angle Find the measure of angle B.

Pythagorean Theorem & Its Converse

Presentation transcript:

Pythagorean Theorem

Right Triangle Hypotenuse Legs Pythagorean Theorem Radical/Radicand VOCABULARY Right Triangle Hypotenuse Legs Pythagorean Theorem Radical/Radicand Square Root

RIGHT TRIANGLE Longest side is the hypotenuse, side c (opposite the 90o angle) The other two sides are the legs, sides a and b Pythagoras developed a formula for finding the length of the sides of any right triangle

RADICAL/RADICAND

SQUARE ROOT Definition: A number the produces a specified quantity when multiplied by itself.

THE PYTHAGOREAN THEOREM “For any right triangle, the sum of the areas of the two small squares is equal to the area of the larger.” a2 + b2 = c2 In different words… If the angle opposite the hypotenuse is a right angle, then a2 + b2 = c2

EXAMPLE #1 If two measures of the sides of a right triangle are known, the Pythagorean Theorem can be used to find the measure of the third side.

EXAMPLE #2 152+82=c2 225+64=c2 289=c2 17=c

YOUR TURN! ☺

Normal: If x, then y. Converse: If y, then x. CONVERSE? Example: If it is raining, then the grass is wet. Converse: If the grass is wet, then it is raining.

CONVERSE OF THE PYTHAGOREAN THEOREM “If a triangle has sides of lengths a, b, and c; and a2 + b2 = c2 then the triangle is a right triangle with hypotenuse of length c.” You can determine if a triangle is a right triangle if the 3 side lengths fit into a2 + b2 = c2

No! This is not a right triangle. EXAMPLE #1 No! This is not a right triangle. 52+72=92 25+49=81?

YOUR TURN! ☺

COMMON PYTHAGOREAN TRIPLES

Find the length of the hypotenuse if 1. a = 12 and b = 16. 122 + 162 = c2 144 + 256 = c2 400 = c2 Take the square root of both sides. 20 = c

Find the length of the hypotenuse if 2. a = 5 and b = 7. 16

Find the length of the hypotenuse given a = 6 and b = 12 180 324 13.42 18

Find the length of the leg, to the. nearest hundredth, if 3 Find the length of the leg, to the nearest hundredth, if 3. a = 4 and c = 10.

Find the length of the leg, to the nearest hundredth, if 4 Find the length of the leg, to the nearest hundredth, if 4. c = 10 and b = 7.

Find the length of the missing side given a = 4 and c = 5 1 3 6.4 9

5. The measures of three sides of a triangle are given below 5. The measures of three sides of a triangle are given below. Determine whether each triangle is a right triangle. 5 , 3, and 8

The rectangular bottom of a box has an interior length of 19 inches and an interior width of 14 inches. A stick is placed in the box along the diagonal of the bottom of the box. Which measurement is closest to the longest possible length for the stick? a2 + b2 = c2 F 12.8 in. G 16.3 in. H 23.6 in. J 33.0 in.

REAL-LIFE APPLICATIONS The Pythagorean theorem has far-reaching ramifications in other fields (such as the arts), as well as practical applications. The theorem is invaluable when computing distances between two points, such as in navigation and land surveying. Another important application is in the design of ramps. Ramp designs for handicap-accessible sites and for skateboard parks are very much in demand. Can you think of other ways the Pythagorean Theorem can be extremely valuable?

Baseball Problem A baseball “diamond” is really a square. You can use the Pythagorean theorem to find distances around a baseball diamond.

BASEBALL PROBLEM The distance between consecutive bases is 90 feet. How far does a catcher have to throw the ball from home plate to second base? 25

BASEBALL PROBLEM To use the Pythagorean theorem to solve for x, find the right angle. Which side is the hypotenuse? Which sides are the legs? Now use: a2 + b2 = c2 26

BASEBALL PROBLEM SOLUTION The hypotenuse is the distance from home to second, or side x in the picture. The legs are from home to first and from first to second. Solution: x2 = 902 + 902 = 16,200 x = 127.28 ft 27

LADDER PROBLEM A ladder leans against a second-story window of a house. If the ladder is 25 meters long, and the base of the ladder is 7 meters from the house, how high is the window? 28

LADDER PROBLEM SOLUTION First draw a diagram that shows the sides of the right triangle. Label the sides: Ladder is 25 m Distance from house is 7 m Use a2 + b2 = c2 to solve for the missing side. Distance from house: 7 meters 29

LADDER PROBLEM SOLUTION b = 24 m How did you do? B 30

DO NOT DO THIS! 31