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.

Slides:

Advertisements

Similar presentations

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

Advertisements

The Pythagorean Theorem and its Converse

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.

Apply the Pythagorean Theorem Chapter 7.1. Sides of a Right Triangle Hypotenuse – the side of a right triangle opposite the right angle and the longest.

Created by G. Antidormi 2003 The Pythagorean Theorem.

The Pythagorean Theorem. Objectives The objective of this lesson is for you to learn and apply the Pythagorean Theorem -- an important relationship between.

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,

Pythagorean Triples In addition to level 3.0 and beyond what was taught in class, the student may:  Make connection with other concepts in math.

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.

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.

Lesson 10.1 The Pythagorean Theorem. The side opposite the right angle is called the hypotenuse. The other two sides are called legs. We use ‘a’ and ‘b’

Pythagorean Theorem.

4.4: THE PYTHAGOREAN THEOREM AND DISTANCE FORMULA

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

Bell Ringer Get out your 10.5/10.7 homework assignment and formula sheet Get out your notebook and prepare to take notes on Section 11.2 What do you know.

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

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

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 called legs. The side.

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

Ch 9.1 The Pythagorean Theorem Definition of the Day Right Triangle Legs of a Triangle Hypotenuse of a Triangle The Pythagorean Theorem.

Section 11.6 Pythagorean Theorem. Pythagorean Theorem: In any right triangle, the square of the length of the hypotenuse equals the sum of the squares.

30°, 60°, and 90° - Special Rule The hypotenuse is always twice as long as the side opposite the 30° angle. 30° 60° a b c C = 2a.

Objective The student will be able to:

1 The Pythagorean Theorem. 2 A B C Given any right triangle, A 2 + B 2 = C 2.

Things to remember: Formula: a 2 +b 2 =c 2 Pythagorean Theorem is used to find lengths of the sides of a right triangle Side across from the right angle.

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

Pythagorean Theorem and it’s Converse. Pythagorean Theorem Pythagorean Theorem: used for right triangles, it is a tool used to solve for a missing side.

Pythagorean Theorem Chapter 3 – 5. What’s a, b, & c? a & b are the two sides that form the 90° angle a & b are also known as “legs” of a right triangle.

1.3 Segments and Their Measures Geometry. Postulates  Rules that are accepted as true without proof  Sometimes they are called axioms.

4.4 Pythagorean Theorem and the Distance Formula Textbook pg 192.

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

8-2 The Pythagorean Theorem and Its Converse The student will be able to: 1.Use the Pythagorean Theorem. 2.Use the Converse of the Pythagorean Theorem.

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.

Pythagorean Theorem & Distance Formula Anatomy of a right triangle The hypotenuse of a right triangle is the longest side. It is opposite the right angle.

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

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.

Find the geometric mean between 9 and 13.

Pythagorean Triples.

The Distance and Midpoint Formulas

SOL 8.10 Pythagorean Theorem.

Objective The student will be able to:

Midpoint And Distance in the Coordinate Plane

Objective The student will be able to:

Notes Over Pythagorean Theorem

Pythagorean Theorem What is it??

Objective The student will be able to:

Objective- To solve problems involving the Pythagorean Theorem.

6-3 The Pythagorean Theorem Pythagorean Theorem.

5-7 The Pythagorean Theorem

5.7: THE PYTHAGOREAN THEOREM (REVIEW) AND DISTANCE FORMULA

5-3: The Pythagorean Theorem

The Pythagorean Theorem and Its Converse

Objective- To solve problems involving the Pythagorean Theorem.

Objective The student will be able to:

Objective Students will be able to:

Objective The student will be able to:

Pythagorean Theorem, its Converse and the coordinate system

Objective The student will be able to:

Objective The student will be able to:

Objective The student will be able to:

Objective The student will be able to:

In a right triangle, the side opposite the right angle is called the hypotenuse. This side is always the longest side of a right triangle. The other.

Objective The student will be able to:

1-6: Midpoint and Distance

Presentation transcript:

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 or supplementary d = 52°, triangles = 180°

Classwork/Homework

REVIEW FROM FRIDAY! Pythagorean Theorem

Right Triangles Hypotenuse – Longest side is the hypotenuse, side c (opposite the 90 o angle) The other two sides are the legs, sides a and b Hypotenuse (c) Leg (a) Leg (b) It doesn’t matter which leg is “a” or “b”. The hypotenuse is always side c!

The Pythagorean Theorem In a RIGHT Triangle, if sides “a” and “b” are the legs and side “c” is the hypotenuse, then a 2 + b 2 = c 2 a b c

The Pythagorean Theorem Find the missing side. a a 2 + b 2 = c 2 a = 17 2 a = 289 a 2 = 64 a = √64 = 8

The Pythagorean Theorem Chris’ window is 12 feet high. If he placed his ladder 9 feet away from the base of the house, how long is the ladder? a 2 + b 2 = c = c = c = c 2 √225 = c 15 feet = c Ladder = c Base = 9 ft Window = 12 ft

The Pythagorean Theorem Three points are located on a coordinate plane. How long is the diagonal formed by the three points? a 9 8 a 2 + b 2 = c = c = c = c 2 c = √145 = b c c We could have used the distance formula to solve this!

PPF RECOGNIZE PYTHAGOREAN TRIPLES* Pythagorean Triples

Pythagorean Triples are three positive whole numbers that fit the rule “ a 2 + b 2 = c 2”. The most famous triple is 3, 4, 5. This means that the legs are 3 & 4, while the hypotenuse is 5. The hypotenuse is the longest side a 2 + b 2 = c = = = 25 This is true, so 3, 4, 5 is a triple!

Pythagorean Triples Any multiple of a Pythagorean Triple is also true. So, any multiple of 3, 4, 5 is also a triple. 6, 8, 10 (multiply by 2) is a triple a 2 + b 2 = c = = = 100 This is true, so 6, 8, 10 is a triple!

Pythagorean Triples Determine whether a triangle with lengths 7, 11, and 12 form a right triangle. (The hypotenuse is always the longest length.) a 2 + b 2 = c = = = 144 This is NOT true, so this is not a right triangle!

Pythagorean Triples Determine whether a triangle with lengths 12, 16, and 20 form a right triangle. (The hypotenuse is always the longest length.) a 2 + b 2 = c = = = 400 This IS true, so this is a right triangle! This is also a multiple of 3, 4, 5 triple!