The Pythagorean Theorem

Slides:

Advertisements

Similar presentations

The Pythagorean Theorem c a b.

Advertisements

PYTHAGOREAN THEOREM.

Pythagorean Theorem Story Problems Goal: Solve for an unknown measurement of using the Pythagorean Theorem.

Real-life Application of the 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 Trig fractions Solving For Angles Solving for Sides Words are Problems?! Other Right Stuff $100 $200 $300 $400 $500 $100 $200 $300 $400 $500.

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

Pythagorean Theorem, Distance Formula and Midpoint Formula.

Applications of the Pythagorean Theorem

The Pythagorean Theorem A tool for right triangle problems only.

5.7 The Pythagorean Theorem. a 2 + b 2 = c 2 The Pythagorean Theorem.

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 Part 2. The bases on a baseball diamond are 90 feet apart. How far is it from home plate to second base? 90 ft c a b.

Pythagorean Theorem.

Special Right Triangles EQ: How do you use the properties of special right triangles in real world applications? M2 Unit 2: Day 2.

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.

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.

Pythagorean Theorem Two sides of a right triangle measure 6 feet and 8 feet. What is the length of the hypotenuse?

Geometry Section 9.2 The Pythagorean Theorem. In a right triangle the two sides that form the right angle are called the legs, while the side opposite.

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.

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.

Pythagorean theorem! By : Katey Lynch. History of the Pythagorean theorem! Well it all started with a Greek mathematician Pythagoras. He discovered something.

Chapter 8: Right Triangles & Trigonometry 8.2 Special Right Triangles.

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

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

The Pythagorean Theorem A tool for right triangle problems.

Pythagorean Theorem Test Review

EQ: What is the relationship between the 3 sides in a right triangle?

The Pythagorean Theorem Part 2. The bases on a baseball diamond are 90 feet apart. How far is it from home plate to second base? 90 ft c a b a² + b² =

The Pythagorean Theorem

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

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

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

Pythagorean Theorem in Context WALK. Problem #1 To get from point A to point B you must avoid walking through a pond. To avoid the pond, you must walk.

How do I use the Pythagorean Theorem to solve problems?

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.

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.

Applying Pythagorean Theorem

The Pythagorean Theorem

Before: April 12, 2016 What is the length of the hypotenuse of

The Pythagorean Theorem

The Pythagorean Theorem

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

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

Pythagorean Theorem Practice, Practice, Practice!.

Pythagorean Theorem.

Pythagorean Theorem.

Pythagorean Theorem.

Bellwork (block 2) Textbook pg 415 (ALL)

Pythagorean Theorem.

Pythagorean Theorem.

The Distance Formula & Pythagorean Theorem

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

Pythagorean Theorem OR.

Sine and Cosine Rule s.small.

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

Applying Pythagorean Theorem

Pythagorean Theorem.

The Pythagorean Theorem

The Pythagorean Theorem

Warm Ups 1. Find the absolute value of -8 – 3i.

Pythagorean Theorem.

Pythagorean Theorem.

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

Pythagorean Theorem & Its Converse

Presentation transcript:

The Pythagorean Theorem

A 15 foot ladder leans up against a building A 15 foot ladder leans up against a building. The foot of the ladder is 5 feet from the base of the building. How high up the wall, to the nearest foot does the ladder reach? a2 + b2 = c2 15 a2 + 52 = 152 ? a2 + 25 = 225 5 a2 = 200 ― √ a = 200 a = 14.1

Tim rode 8 miles due north, then 3 miles due east Tim rode 8 miles due north, then 3 miles due east. How far, to the nearest mile, is Tim from where he started? 3 a2 + b2 = c2 82 + 32 = c2 64 + 9 = c2 8 ? ― 73 = c2 √ 73 = c 8.5 = c

Laptop screen sizes are determined by the length of the diagonal portion of the screen, rounded to the nearest whole number. A laptop screen has a 10 inch width and the height measures 8 inches. Calculate the screen size. a2 + b2 = c2 10 82 + 102 = c2 ? 64 + 100 = c2 8 164 = c2 ― √ 164 = c 12.8 = c

A baseball diamond is a square that is 90’ on each side A baseball diamond is a square that is 90’ on each side. If a player throws the ball from 2nd base to home, how far will the ball travel? a2 + b2 = c2 90 902 + 902 = c2 8100 + 8100 = c2 ? 16200= c2 ― 90 √ 16200 = c 127.3 = c

An isosceles triangle has congruent sides of 20 cm. The base is 10 cm An isosceles triangle has congruent sides of 20 cm. The base is 10 cm. What is the height of the triangle? a2 + b2 = c2 52 + b2 = 202 20 20 25 + b2 = 400 ? b2 = 375 5 ― 10 √ b = 375 a = 19.3

― √ Distance Across Distance Around a2 + b2 = c2 10 + 15 =25 You can get around a rectangular park by walking up one side that is 10 feet long and along another side that is 15 feet long. How much distance would you save if you walked across the park instead of around it? Distance Across Distance Around a2 + b2 = c2 10 + 15 =25 102 + 152 = c2 ? 15 Distance saved 100 + 225 = c2 325 = c2 ― 25 - 18 = 7 √ 325 = c 10 18 = c