Honors Geometry Section 5.4 The Pythagorean Theorem

Slides:

Advertisements

Similar presentations

Splash Screen. Lesson Menu Five-Minute Check (over Lesson 8–1) Then/Now New Vocabulary Theorem 8.4: Pythagorean Theorem Proof: Pythagorean Theorem Example.

Advertisements

Quiz Review 7.1,7.2, and 7.4.

The Pythagorean Theorem and its Converse

Keystone Geometry 1 The Pythagorean Theorem. Used to solve for the missing piece of a right triangle. Only works for a right triangle. Given any right.

Objectives Use the Pythagorean Theorem and its converse to solve problems. Use Pythagorean inequalities to classify triangles.

The Pythagorean Theorem Holt Geometry Warm Up Warm Up Lesson Presentation Lesson Presentation Lesson Quiz Lesson Quiz Holt McDougal Geometry Pythagorean.

Warm UP. Essential Question How can I solve for side lengths of a right triangle and how can you use side lengths to determine whether a triangle is acute,

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

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.

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’

The Pythagorean Theorem

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

8-1 The Pythagorean Theorem and Its Converse. Parts of a Right Triangle In a right triangle, the side opposite the right angle is called the hypotenuse.

Pythagorean Theorem and Its Converse Objective To use the Pythagorean Theorem and its converse Essential Understanding: If you know the lengths of any.

The Pythagorean Theorem

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

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

9/23/ : The Pythagoream Theorem 5.4: The Pythagorean Theorem Expectation: G1.2.3: Know a proof of the Pythagorean Theorem and use the Pythagorean.

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.

+ Warm Up B. + Homework page 4 in packet + #10 1. Given 2. Theorem Given 4. Corresponding angles are congruent 5. Reflexive 6. AA Similarity 7.

Do Now 5/16/11 Copy HW in your planner. Copy HW in your planner. Text p. 467, #8-30 evens, & 19 Text p. 467, #8-30 evens, & 19 Be ready to copy POTW #6.

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.

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

Triangles. 9.2 The Pythagorean Theorem In a right triangle, the sum of the legs squared equals the hypotenuse squared. a 2 + b 2 = c 2, where a and b.

Pythagorean Theorem Unit 7 Part 1. The Pythagorean Theorem The sum of the squares of the legs of a right triangle is equal to the square of the hypotenuse.

Geometry Section 9.3 Pythagorean Theorem Converse.

The Pythagorean Theorem

12/24/2015 Geometry Section 9.3 The Converse of the Pythagorean Theorem.

Pythagorean Theorem and Its Converse Chapter 8 Section 1.

Pythagorean Theorem Theorem 8-1: Pythagorean Theorem – In a right triangle, the sum of the squares of the lengths of the legs is equal to the square of.

3/11-3/ The Pythagorean Theorem. Learning Target I can use the Pythagorean Theorem to find missing sides of right triangles.

Section 8-3 The Converse of the Pythagorean Theorem.

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.

Example 1 1.What is the area of a square with a side length of 4 inches? x inches? 2.What is the side length of a square with an area of 25 in 2 ? x in.

Do Now 5/11/10 Copy HW in your planner. Copy HW in your planner. –Text p. 740, #4-22 evens, #34 In your notebooks, simplify the following expressions.

Chapter 7 Right Triangles and Trigonometry Objectives: Use calculator to find trigonometric ratios Solve for missing parts of right triangles.

HONORS GEOMETRY 8.2. The Pythagorean Theorem. Do Now: Find the missing variables. Simplify as much as possible.

Holt Geometry 5-7 The Pythagorean Theorem Warm Up Classify each triangle by its angle measures Simplify 4. If a = 6, b = 7, and c = 12, find.

Geometry Section 7.1 Apply the Pythagorean Theorem.

Converse of the Pythagorean Theorem

Objectives Use the Pythagorean Theorem and its converse to solve problems. Use Pythagorean inequalities to classify triangles.

8.1 Pythagorean Theorem and Its Converse

The Pythagorean Theorem

Find the geometric mean between 9 and 13.

Pythagorean Theorem and it’s Converse

Rules of Pythagoras All Triangles:

The Converse of the Pythagorean Theorem

Section 7.2 Pythagorean Theorem and its Converse Objective: Students will be able to use the Pythagorean Theorem and its Converse. Warm up Theorem 7-4.

The Pythagorean Theorem

Bellringer Simplify each expression 5 ∙ ∙ 8.

WARM UP Decide whether the set of numbers can represent the side lengths of a triangle. 2, 10, 12 6, 8, 10 5, 6, 11.

Lesson 8 – 2 The Pythagorean Theorem and Its Converse

8-2 The Pythagorean Theorem and Its Converse

The Pythagorean Theorem

5.7: THE PYTHAGOREAN THEOREM (REVIEW) AND DISTANCE FORMULA

The Pythagorean Theorem

7-1 and 7-2: Apply the Pythagorean Theorem

8.1 Pythagorean Theorem and Its Converse

The Pythagorean Theorem

Solve for the unknown side or angle x

Pythagorean Theorem OR.

WARM UP Decide whether the set of numbers can represent the side lengths of a triangle. 2, 10, 12 6, 8, 10 5, 6, 11.

The Pythagorean Theorem

Pythagorean Theorem & Its Converse

7-2 PYTHAGOREAN THEOREM AND ITS CONVERSE

Presentation transcript:

Honors Geometry Section 5.4 The Pythagorean Theorem

In a right triangle the two sides that form the right angle are called the legs, while the side opposite the right angle is called the hypotenuse.

Consider placing four congruent right triangles with legs a and b and hypotenuse c as shown at the right. Notice that the large figure is a square. Using the formula for the area of a square (A = s2) what is its area?

We can also find the area of the large figure by adding the areas of the smaller square and the four triangles. The area of a triangle is found by the formula .

If we set the two expressions for the area of the larger square equal to each other, we get:

The Pythagorean Theorem For any right triangle with hypotenuse c and legs a and b, the sum of the squares of the legs ( )is equal to the square of the hypotenuse ( ).

A Pythagorean Triple is three whole numbers that could be the sides of a right triangle.

Example: If a 25-foot ladder is leaning against a house and the bottom of the ladder is 9 feet away from the house, how far up the side of the house is the top of the ladder? Round to the nearest 1000th.

The converse of the Pythagorean Theorem is also true The converse of the Pythagorean Theorem is also true. Pythagorean Theorem Converse If the square of the largest side of a triangle equals the sum of the squares of the other two sides, then the triangle is a right triangle.

If a triangle is not a right triangle, then it must be either acute or obtuse.

Examples: Is a triangle with the given sides acute, right, obtuse or can’t exist. If the triangle cannot exist, explain why.

Examples: Is a triangle with the given sides acute, right, obtuse or can’t exist. If the triangle cannot exist, explain why.