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

Slides:

Advertisements

Similar presentations

Advertisements

The Pythagorean Theorem and its Converse

Honors Geometry Section 5.4 The Pythagorean Theorem

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.

TODAY IN GEOMETRY… Warm Up: Simplifying Radicals

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

EXAMPLE 2 Standardized Test Practice SOLUTION =+.

EXAMPLE 2 Standardized Test Practice SOLUTION =+.

1 9.1 and 9.2 The Pythagorean Theorem. 2 A B C Given any right triangle, A 2 + B 2 = C 2.

10.5 – The Pythagorean Theorem. leg legleg hypotenuse hypotenuse leg legleg.

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

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. PYTHAGOREAN THEOREM REAL LIFE EXAMPLE The following is a rule of thumb for safely positioning a ladder: The distance from the.

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

Pythagorean Theorem Use the Pythagorean Theorem to find the missing length of the right triangle. 1.

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.

Pythagorean Theorem And Its Converse

7.1 – Apply the Pythagorean Theorem. Pythagorean Theorem: leg hypotenuse a b c c 2 = a 2 + b 2 (hypotenuse) 2 = (leg) 2 + (leg) 2 If a triangle is a right.

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.

Apply the Pythagorean Theorem

Warm Up: Find the geometric mean of: a) 12 and 18b) 54 and 36 c) 25 and 49.

1. Solve x2 = 100. ANSWER 10, –10 2. Solve x2 + 9 = 25. ANSWER 4, –4

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

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.

The Pythagorean Theorem

Welcome Back Review. If c is the measure of the hypotenuse, find each missing side: 1. a = 12, b = 9, c = ?c = a = 8, b = ?, c = 21b = 19.4.

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.

Warm-Up Exercises 2. Solve x = 25. ANSWER 10, –10 ANSWER 4, –4 1. Solve x 2 = 100. ANSWER Simplify 20.

Converse of Pythagorean Theorem

11.2 Pythagorean Theorem. Applies to Right Triangles Only! leg Leg a hypotenuse c Leg b.

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 What is the Pythagorean Theorem? You place a 10-foot ladder against a wall. If the base of the ladder is 3 feet from the wall, how high up the.

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.

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

Objective The learner will solve problems using the Pythagorean Theorem.

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

10-2 The Pythagorean Theorem Hubarth Algebra. leg hypotenuse Pythagorean Theorem In any right triangle, the sum of the squares of the lengths of the legs.

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

Objective: To use the Pythagorean Theorem to solve real world problems. Class Notes Sec 9.2 & a b c a short leg b long leg c hypotenuse 2. Pythagorean.

Geometry Section 7.1 Apply the Pythagorean Theorem.

Find the geometric mean between 9 and 13.

Warm-Up Find the group members with the same letter on their worksheet as you. Complete problems #3 & #4. Take your homework with you to be checked!

1. Solve x2 = 100. ANSWER 10, –10 2. Solve x2 + 9 = 25. ANSWER 4, –4

4.5 The Converse of the Pythagorean Theorem

The Pythagorean Theorem

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.

Section 1 – Apply the Pythagorean Theorem

Notes Over Pythagorean Theorem

8.2 The Pythagorean Theorem & Its Converse

Pythagorean Theorem What is it??

Unit 5: Pythagorean Theorem

Pythagorean Theorem Practice, Practice, Practice!.

6-3 The Pythagorean Theorem Pythagorean Theorem.

15.6 – Radical Equations and Problem Solving

5-7 The Pythagorean Theorem

The Pythagorean Theorem

7.1 Apply the Pythagorean theorem.

Solve for the unknown side or angle x

1. Solve x2 = 100. ANSWER 10, –10 2. Solve x2 + 9 = 25. ANSWER 4, –4

THE PYTHAGOREAN THEOREM

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

Chapter 10 Vocabulary 1.) hypotenuse 2.) leg 3.) Pythagorean Theorem

Presentation transcript:

1 The Pythagorean Theorem

2 A B C Given any right triangle, A 2 + B 2 = C 2

3 Example A B C In the following figure if A = 3 and B = 4, Find C. A 2 + B 2 = C = C = C 2 5 = C

4 Practice 1) A = 8, B = 15, Find C 2) A = 7, B = 24, Find C 3) A = 9, B= 40, Find C 4) A = 10, B = 24, Find C 5)A = 6, B = 8, Find C 6) A = 9, B = 12, Find C 1) A = 8, B = 15, Find C 2) A = 7, B = 24, Find C 3) A = 9, B= 40, Find C 4) A = 10, B = 24, Find C 5)A = 6, B = 8, Find C 6) A = 9, B = 12, Find C A B C C = 17 C = 25 C = 41 C = 26 C = 10 C = 15

5 Example A B C In the following figure if B = 5 and C = 13, Find A. A 2 + B 2 = C 2 A = 13 2 A = 169 A 2 = 144 A = 12

6 Practice 1)A=8, C =10, Find B 2)A=15, C=17, Find B 3)B =10, C=26, Find A 4)A =12, C=16, Find B 5) B =5, C=10, Find A 6) A=11, C=21, Find B 1)A=8, C =10, Find B 2)A=15, C=17, Find B 3)B =10, C=26, Find A 4)A =12, C=16, Find B 5) B =5, C=10, Find A 6) A=11, C=21, Find B A B C B = 6 B = 8 A = 24 B = 10.6 A = 8.7 B = 17.9

“Real-World” 7 The top of a ladder rests against a wall, 23 feet above the ground. The base of the ladder is 6 feet away from the wall. What is the length of the ladder? Step 1: Draw a sketch and label the parts. Step 2: Determine whether you are looking for the leg or hypotenuse of the right triangle. Step 3: Solve the missing length.

AREA 8 Find the area of each figure 1.2.

9 Given the lengths of three sides, how do you know if you have a right triangle? A B C Given A = 6, B=8, and C=10, describe the triangle. A 2 + B 2 = C = = = 100 This is true, so you have a right triangle. This is true, so you have a right triangle.

10 If C 2 < A 2 + B 2, then you have an acute triangle. Given A = 4, B = 5, and C =6, describe the triangle. C 2 = A 2 + B = = < < 41, so we have an acute triangle. Given A = 4, B = 5, and C =6, describe the triangle. C 2 = A 2 + B = = < < 41, so we have an acute triangle. A B C

11 If C 2 > A 2 + B 2, then you have an obtuse triangle. Given A = 4, B = 6, and C =8, describe the triangle. C 2 = A 2 + B = = > > 52, so we have an obtuse triangle. Given A = 4, B = 6, and C =8, describe the triangle. C 2 = A 2 + B = = > > 52, so we have an obtuse triangle. A C B

12 Describe the following triangles as acute, right, or obtuse 1)A=10, B=15, C=20 2) A=2, B=5, C=6 3) A=12, B=16, C=20 4) A=11, B=12, C=14 5) A=2, B=3, C=4 6) A=1, B=7, C=7 1)A=10, B=15, C=20 2) A=2, B=5, C=6 3) A=12, B=16, C=20 4) A=11, B=12, C=14 5) A=2, B=3, C=4 6) A=1, B=7, C=7 A B C obtuse acute obtuse right obtuse acute