Find Missing Measures Using the Pythagorean Theorem A

  • Slides: 22
Download presentation

Find Missing Measures Using the Pythagorean Theorem A. Find x. The side opposite the

Find Missing Measures Using the Pythagorean Theorem A. Find x. The side opposite the right angle is the hypotenuse, so c = x. a 2 + b 2= c 2 Pythagorean Theorem 42 + 72= c 2 a = 4 and b = 7

Find Missing Measures Using the Pythagorean Theorem 65 = c 2 Simplify. Take the

Find Missing Measures Using the Pythagorean Theorem 65 = c 2 Simplify. Take the positive square root of each side. Answer:

Find Missing Measures Using the Pythagorean Theorem B. Find x. The hypotenuse is 12,

Find Missing Measures Using the Pythagorean Theorem B. Find x. The hypotenuse is 12, so c = 12. a 2 + b 2= c 2 Pythagorean Theorem x 2 + 82 = 122 b = 8 and c = 12

Find Missing Measures Using the Pythagorean Theorem x 2 + 64 = 144 Simplify.

Find Missing Measures Using the Pythagorean Theorem x 2 + 64 = 144 Simplify. x 2 Subtract 64 from each side. = 80 Take the positive square root of each side and simplify. Answer:

A. Find x. A. B. C. D. A B C D

A. Find x. A. B. C. D. A B C D

B. Find x. A. B. C. D. A B C D

B. Find x. A. B. C. D. A B C D

Use a Pythagorean Triple Use a Pythagorean triple to find x. Explain your reasoning.

Use a Pythagorean Triple Use a Pythagorean triple to find x. Explain your reasoning.

Use a Pythagorean Triple Notice that 24 and 26 are multiples of 2 :

Use a Pythagorean Triple Notice that 24 and 26 are multiples of 2 : 24 = 2 ● 12 and 26 = 2 ● 13. Since 5, 12, 13 is a Pythagorean triple, the missing length x is 2 ● 5 or 10. Answer: Check: x = 10 2 ? 2 24 + 10 = 262 676 = 676 Simplify. Pythagorean Theorem

Use a Pythagorean triple to find x. A. 10 B. 15 C. 18 D.

Use a Pythagorean triple to find x. A. 10 B. 15 C. 18 D. 24 A. B. C. D. A B C D

A 20 -foot ladder is placed against a building to reach a window that

A 20 -foot ladder is placed against a building to reach a window that is 16 feet above the ground. How many feet away from the building is the bottom of the ladder? A 3 B 4 C 12 D 15

A 10 -foot ladder is placed against a building. The base of the ladder

A 10 -foot ladder is placed against a building. The base of the ladder is 6 feet from the building. How high does the ladder reach on the building? A. 6 ft B. 8 ft C. 9 ft D. 10 ft A. B. C. D. A B C D

Classify Triangles A. Determine whether 9, 12, and 15 can be the measures of

Classify Triangles A. Determine whether 9, 12, and 15 can be the measures of the sides of a triangle. If so, classify the triangle as acute, right, or obtuse. Justify your answer. Step 1 Determine whether the measures can form a triangle using the Triangle Inequality Theorem. 9 + 12 > 15 9 + 15 > 12 + 15 > 9 The side lengths 9, 12, and 15 can form a triangle.

Classify Triangles Step 2 Classify the triangle by comparing the square of the longest

Classify Triangles Step 2 Classify the triangle by comparing the square of the longest side to the sum of the squares of the other two sides. 2 ? c b 2. ? 152 = a 2 + b 2 Compare c 2 and a 2 + = 122 + 92 Substitution 225 = 225 Simplify and compare. Answer: Since c 2 = a 2 + b 2, the triangle is right.

Classify Triangles B. Determine whether 10, 11, and 13 can be the measures of

Classify Triangles B. Determine whether 10, 11, and 13 can be the measures of the sides of a triangle. If so, classify the triangle as acute, right, or obtuse. Justify your answer. Step 1 Determine whether the measures can form a triangle using the Triangle Inequality Theorem. 10 + 11 > 13 10 + 13 > 11 + 13 > 10 The side lengths 10, 11, and 13 can form a triangle.

Classify Triangles Step 2 Classify the triangle by comparing the square of the longest

Classify Triangles Step 2 Classify the triangle by comparing the square of the longest side to the sum of the squares of the other two sides. 2 ? c b 2. ? 132 = a 2 + b 2 Compare c 2 and a 2 + = 112 + 102 Substitution 169 < 221 Simplify and compare. Answer: Since c 2 < a 2 + b 2, the triangle is acute.

A. Determine whether the set of numbers 7, 8, and 14 can be the

A. Determine whether the set of numbers 7, 8, and 14 can be the measures of the sides of a triangle. If so, classify the triangle as acute, right, or obtuse. Justify your answer. A. yes, acute B. yes, obtuse C. yes, right D. not a triangle A. B. C. D. A B C D

B. Determine whether the set of numbers 14, 18, and 33 can be the

B. Determine whether the set of numbers 14, 18, and 33 can be the measures of the sides of a triangle. If so, classify the triangle as acute, right, or obtuse. Justify your answer. A. yes, acute B. yes, obtuse C. yes, right D. not a triangle A. B. C. D. A B C D

SHAPE SPACE Pythagorean Theorem Pythagorean Theorem Pythagorean TheoremSHAPE SPACE Pythagorean Theorem Pythagorean Theorem Pythagorean Theorem
PYTHAGOREAN THEOREM Application Using the Pythagorean Theorem forPYTHAGOREAN THEOREM Application Using the Pythagorean Theorem for
The Pythagorean Theorem The Pythagorean Theorem For anyThe Pythagorean Theorem The Pythagorean Theorem For any
Pythagorean Theorem History of Pythagorean Theorem Review ThePythagorean Theorem History of Pythagorean Theorem Review The
Lesson 7 2 Pythagorean Theorem Pythagorean Theorem rightLesson 7 2 Pythagorean Theorem Pythagorean Theorem right
Lesson 11 4 Pythagorean Theorem The Pythagorean theoremLesson 11 4 Pythagorean Theorem The Pythagorean theorem
The Pythagorean Theorem 1 The Pythagorean Theorem GivenThe Pythagorean Theorem 1 The Pythagorean Theorem Given
Pythagorean Theorem 6 3 The Pythagorean Theorem WarmPythagorean Theorem 6 3 The Pythagorean Theorem Warm
PYTHAGOREAN THEOREM PROJECT Pythagorean Theorem Project Due WednesdayPYTHAGOREAN THEOREM PROJECT Pythagorean Theorem Project Due Wednesday
The Pythagorean Theorem Objectives Use the Pythagorean TheoremThe Pythagorean Theorem Objectives Use the Pythagorean Theorem
Pythagorean Theorem 6 3 The Pythagorean Theorem WarmPythagorean Theorem 6 3 The Pythagorean Theorem Warm
The Pythagorean Theorem Polygons Area JEOPARDY PYTHAGOREAN THEOREMThe Pythagorean Theorem Polygons Area JEOPARDY PYTHAGOREAN THEOREM
PROVING THE PYTHAGOREAN THEOREM The Pythagorean Theorem isPROVING THE PYTHAGOREAN THEOREM The Pythagorean Theorem is
Pythagorean Theorem homework Pythagorean theorem worksheet 1 9Pythagorean Theorem homework Pythagorean theorem worksheet 1 9
The Pythagorean Theorem Applications The Pythagorean theorem hasThe Pythagorean Theorem Applications The Pythagorean theorem has
Pythagorean Theorem Pythagorean Theorem Word Problems A squarePythagorean Theorem Pythagorean Theorem Word Problems A square
Pythagorean Theorem and Its Converse Pythagorean Theorem IfPythagorean Theorem and Its Converse Pythagorean Theorem If
Lesson 8 7 The Pythagorean Theorem The PythagoreanLesson 8 7 The Pythagorean Theorem The Pythagorean
8 1 Pythagorean Theorem and Its Converse Pythagorean8 1 Pythagorean Theorem and Its Converse Pythagorean
Pythagorean Theorem Distance Formula and Midpoint Formula PythagoreanPythagorean Theorem Distance Formula and Midpoint Formula Pythagorean
4 8 Pythagorean Theorem 4 8 The Pythagorean4 8 Pythagorean Theorem 4 8 The Pythagorean