Objectives Vocabulary Example 1 Example 2 Example 3
Objectives Vocabulary Example 1 Example 2 Example 3 Quick Quiz
• To determine a graphical understanding of the Pythagorean Theorem • To develop an understanding of how a right triangle and squares are related through the Pythagorean Theorem • To use the Pythagorean Theorem to determine the missing side length or hypotenuse length of a right triangle • To determine and use the distance formula
• right triangle • hypotenuse • leg • Pythagorean Theorem • distance formula
The measures of three sides of a triangle are 24 inches, 7 inches, and 25 inches. Determine whether the triangle is a right triangle. c 2 = a 2 + b 2 Pythagorean Theorem ? Replace a with 7, b with 24, and c with 25. ? 625 = 49 + 576 Evaluate 252, 72, and 242. 625 = 625 Simplify. 252 = 72 + 242 Pythagorean Theorem
Answer: The triangle is a right triangle. Pythagorean Theorem
The measures of three sides of a triangle are 13 inches, 5 inches, and 12 inches. Determine whether the triangle is a right triangle. A. It is a right triangle. B. It is not a right triangle. C. not enough information to determine 1. 2. 3. A B C
The cross-section of a camping tent is shown below. Find the width of the base of the tent. A. 6 ft B. 8 ft C. 10 ft D. 12 ft
Read the Item From the diagram, you know that the tent forms two congruent right triangles. Let a represent half the base of the tent. Then w = 2 a.
Solve the Item Use the Pythagorean Theorem. c 2 = a 2 + b 2 Write the relationship. 102 = a 2 + 82 c = 10 and b = 8 100 = a 2 + 64 Evaluate 102 and 82. 100 – 64 = a 2 + 64 – 64 36 = a 2 =a 6=a Subtract 64 from each side. Simplify. Definition of square root Simplify.
The width of the base of the tent is 2 a or (2)6 = 12 feet. Answer: Therefore, choice D is correct.
This diagram shows the cross-section of a roof. How long is each rafter, r? A. 15 ft B. 18 ft C. 20 ft D. 22 ft 1. 2. 3. 4. A B C D
Nikki kicks a ball from a position that is 2 yards behind the goal line and 4 yards from the side line (– 2, 4). The ball lands 8 yards past the goal line and 2 yards from the same side line (8, 2). What distance, to the nearest tenth, was the ball kicked?
Distance Formula (x 1, y 1) = (– 2, 4) (x 2, y 2) = (8, 2) Simplify. Evaluate powers. Simplify. d ≈ 10. 2 Answer: 10. 2 yards
MAPS The map of a college campus shows Gilmer Hall at (7, 3) and Watson House dormitory at (5, 4). If each unit on the map represents 0. 1 mile, what is the distance between these buildings? A. 0. 2 mi B. 0. 5 mi C. 2. 2 mi D. 5 mi 1. 2. 3. 4. A B C D
The sides of the right triangle are labeled. Find the hypotenuse. A. 4 mm B. approximately 3. 6 mm C. approximately 4. 6 mm D. 6 mm 1. 2. 3. 4. A B C D
If a triangle with squares attached have areas of 6 square units for the smallest square and 10 square units for the largest square, what is the missing area? A. 8 square units B. 16 square units C. 4 square units D. 12 square units 1. 2. 3. 4. A B C D
A right triangle has legs that measure 1 cm and 12 cm. What is the measure of the hypotenuse? A. 21, 025 cm B. 145 cm C. approximately 11. 8 cm D. approximately 12. 04 cm 1. 2. 3. 4. A B C D
Hsin Lee wants to purchase a television that will fit into an entertainment center that has an opening of 30 inches by 40 inches. The size of a television is given in inches, and that number represents the diagonal of the screen. What is the largest television Hsin Lee can purchase? A. 70 in. B. 65 in. C. 50 in. D. 120 in. 1. 2. 3. 4. A B C D
Image Bank Math Tools Multilingual e-Glossary Rational Numbers Square Roots Pythagorean Theorem
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