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

Slides:

Advertisements

Similar presentations

Objective- To solve problems involving the Pythagorean Theorem.

Advertisements

The Pythagorean Theorem c a b.

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

Jeopardy Review Find the Missing Leg / Hypotenuse Pythagorean Theorem Converse Distance Between 2 Points Everybody’s Favorite Similar T riangles Q $100.

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.

Pythagorean Theorem, Distance Formula and Midpoint Formula.

What is the difference between a new penny and an old quarter? Only 4 Gen!uses.

Warm up Write the equation of the line that: 1. Is parallel to y = 3 and goes through the point (2, -4) 2. Is perpendicular to y = 2x + 6 and goes through.

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.

Pythagorean Theorem.

Objective The student will be able to: use the Pythagorean Theorem Designed by Skip Tyler, Varina High School.

Pythagorean Theorem As posted by: oints/math/pythagorean.html.

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.

Learning Target: I can solve problems involving the Pythagorean Theorem. For Right Triangles Only! leg hypotenuse - always opposite the right angle.

Pythagorean Theorem This curriculum was written with funding of the Tennessee Department of Labor and Workforce Development and may not be reproduced in.

Objective The student will be able to:

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.

Lesson #6: Triangles & Pythagorean Theorem

Sec: 7.1 and 7-2 Sol: G.7. Find the geometric mean between each pair of numbers. 4 and 9.

Solve the first 4 questions on your worksheet.

Warm up r = -3 k = -3 x = – 6r = 2r k – 5 = 7k + 7

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.

The Distance Formula & Pythagorean Theorem Day 90 Learning Target : Students can find the distance between 2 points using the distance formula.

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

Warm up Solve – 6r = 2r k – 5 = 7k (x + 4) = 6x r = -3 k = -3 x = 2.

Do Now: A golf ball is launched at 20 m/s at an angle of 38˚ to the horizontal. 1.What is the vertical component of the velocity? 2.What is the horizontal.

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.

Section 8-1. Find the geometric mean between each pair of numbers. 4 and 9.

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 Solve – 6r = 2r k – 5 = 7k (x + 4) = 6x r = -3 k = -3 x = 2.

Warm up Solve – 6r = 2r k – 5 = 7k (x + 4) = 6x r = -3 k = -3 x = 2.

Pre-Algebra Q4W1: Pythagorean Theorem Objective: I can apply the Pythagorean Theorem to determine unknown side lengths in right triangles.

Parts of a Right Triangle A B C Leg Hypotenuse Acute Angle Right Angle Acute Angle R e m e m b e r t h a t t h e h y p o t e n u s e i s a l w a y s t.

The Pythagorean Theorem

The Pythagorean Theorem

The Distance and Midpoint Formulas

The Pythagorean Theorem

SOL 8.10 Pythagorean Theorem.

Pythagorean Theorem: Explanation and Application

The Pythagorean Theorem Mr. Clutter VMS Library

The Pythagorean Theorem

The Pythagorean Theorem Mr. Clutter VMS Library

Pythagorean Theorem Converse

Pythagorean Theorem What is it??

Pythagorean Theorem Practice, Practice, Practice!.

Objective- To solve problems involving the Pythagorean Theorem.

Pythagorean Theorem.

5.7: THE PYTHAGOREAN THEOREM (REVIEW) AND DISTANCE FORMULA

The Pythagorean Theorem

Pythagorean Theorem.

Pythagorean Theorem.

Objective- To solve problems involving the Pythagorean Theorem.

Pythagorean Theorem.

The Distance Formula & Pythagorean Theorem

Warm up r = -3 k = -3 x = – 6r = 2r k – 5 = 7k + 7

The Pythagorean Theorem

Solve for the unknown side or angle x

The Pythagorean Theorem

Pythagorean Theorem, its Converse and the coordinate system

Warm up r = -3 k = -3 x = – 6r = 2r k – 5 = 7k + 7

Objective- To solve problems involving the Pythagorean Theorem.

Pythagorean Theorem.

Pythagorean Theorem.

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

Pythagorean Theorem & Its Converse

Presentation transcript:

Sec 6.6 Pythagorean Theorem

Objective- To solve problems involving the Pythagorean Theorem. For Right Triangles Only! leg hypotenuse - always opposite to the right angle

Objective- To solve problems involving the Pythagorean Theorem. For Right Triangles Only! Leg leg hypotenuse

Leg 2 Objective- To solve problems involving the Pythagorean Theorem. For Right Triangles Only! hypotenuse Leg 1

Leg 2 Hyp Pythagorean Theorem Objective- To solve problems involving the Pythagorean Theorem. For Right Triangles Only! (Leg1) 2 + (leg2) 2 = (Hyp) 2

6 8 x Solve for x. (Leg1) 2 + (leg2) 2 = (Hyp) 2 Line Segment can’t be negative.

4 7 y Solve for y. (Leg1) 2 + (leg2) 2 = (Hyp) 2 Line Segment can’t be negative.

6 t 15 Solve for t. (Leg1) 2 + (leg2) 2 = (Hyp) 2 Line Segment can’t be negative.

Pythagorean Triples

Pythagorean Triples

To the nearest tenth of a foot, find the length of the diagonal of a rectangle with a width of 4 feet and a length of 10 feet. 4 ft. 10 ft. x (Leg1) 2 + (leg2) 2 = (Hyp) 2

20 miles A car drives 20 miles due east and then 45 miles due south. To the nearest hundredth of a mile, how far is the car from its starting point? 45 miles x

Application 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.

Wall Ladder HYP Leg 1 Leg 2

Informal Proof #1 Inscribe a square within the square.

a b a a a b b b c c c c Informal Proof #1

a b a a a b b b c c c c a b c

b a a a b b c c c a b c

b a a a b b c c c a b c a b c

b a a b c c a b c a b c

b a a b c c a b c a b c b a c

a b c a b c a b c b a c

a b c a b c a b c b a c a b c

a b c a b c b a c a b c

a b c a b c b a c a b c

a b c a b c b a c a b c a b c

a b c b a c a b c a b c a b c

b a c a b c a b c a b c a b c

b a c a b c a b c a b c b a c

a b c a b c a b c b a c

a b a a a b b b c c c c Informal Proof #2 a + b Total Purple Yellow Area Area Area - = - =