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

Slides:

Advertisements

Similar presentations

Objective- To solve problems involving the Pythagorean Theorem.

Advertisements

Phythagoras Solving a missing side of a right angled triangle. Miss Hudson’s Maths.

The Pythagorean Theorem c a b.

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

PYTHAGOREAN THEOREM.

(3, 4, 5)(6, 8, 10)(12, 16, 20) (5, 12, 13)(10, 24, 26) (7, 24, 25) (8, 15, 17) (9, 40, 41) (11, 60, 61) (12, 35, 37) (20, 21, 29) PYTHAGOREAN TRIPLES.

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.

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

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

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. The Right Triangle A right triangle is a triangle that contains one right angle. A right angle is 90 o Right Angle.

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.

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

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

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.

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.

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.

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

Solve the first 4 questions on your worksheet.

By Holly Peters and Adelya Baban

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.

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 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.

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

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

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

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

If a2 + b2 = c2, then the triangle is a RIGHT TRIANGLE.

Pythagorean Theorem What is it??

Objective- To solve problems involving the Pythagorean Theorem.

Pythagorean Theorem.

The Pythagorean Theorem

Pythagorean Theorem.

Pythagorean Theorem.

Objective- To solve problems involving the Pythagorean Theorem.

Pythagorean Theorem.

The Distance Formula & Pythagorean Theorem

The Pythagorean Theorem

FAMOUS PYTHAGOREAN TRIPLES:

Solve for the unknown side or angle x

The Pythagorean Theorem

Pythagorean Theorem, its Converse and the coordinate system

Objective- To solve problems involving the Pythagorean Theorem.

Applying Pythagorean Theorem

Pythagorean Theorem.

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

Presentation transcript:

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

Objective- To find the missing side of a right triangle by using Pythagorean Theorem. For Right Triangles Only! leg hypotenuse - always opposite to the right angle

Objective- To find the missing side of a right triangles by using Pythagorean Theorem. For Right Triangles Only! Leg leg hypotenuse

Leg 2 Objective- To find the missing side of a right triangles by using Pythagorean Theorem. For Right Triangles Only! hypotenuse Leg 1

Leg 2 Hyp Pythagorean Theorem Objective- To find the missing side of a right triangles by using 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. (Leg 2) (Leg 1) (Hyp)

4 7 y Solve for y. (Leg1) 2 + (leg2) 2 = (Hyp) 2 Line Segment can’t be negative. (Hyp) (Leg 2) (Leg 1)

6 t 15 Solve for t. (Leg1) 2 + (leg2) 2 = (Hyp) 2 Line Segment can’t be negative. (Hyp) (Leg 1) (Leg 2)

Pythagorean Triples

Pythagorean Triples Leg Leg Hyp

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.

Steps of Solving Pythagorean Word Problems 1. Draw and Label the diagram. (Leg 1, Leg 2 and Hypotenuse) 2. Write out (Leg 1) 2 + (leg 2) 2 = (Hyp) 2 3. Set up the equation. 4. Solve for the unknown. 5. Write a conclusion statement.

Wall Ladder HYP Leg 1 Leg 2 (Leg1) 2 + (leg2) 2 = (Hyp) 2 Diagram: #1 & #3

Soccer Field Diagram Leg 1 = 120 Leg 2 = 90 (Leg1) 2 + (leg2) 2 = (Hyp) 2 #2

Rectangle & Diagonal (#4 & #5) (Leg 1 = __) (Leg 2 = __) Hyp = ___ Width = Leg Lenth = Leg Diagonal = Hypotenuse

#8

Square vs. Diagonal (Ex. Baseball Diamond) HOME Second

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 - = - =