lesson menu main idea and new vocabulary ngsss key concept:pythagorean theorem example 1:find a...
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Main Idea and New Vocabulary
NGSSS
Key Concept: Pythagorean Theorem
Example 1:Find a Missing Length
Example 2: Find a Missing Length
Key Concept: Converse of Pythagorean Theorem
Example 3: Identify a Right Triangle
Five-Minute Check
• Use the Pythagorean Theorem.
• legs
• hypotenuse
• Pythagorean Theorem
• converse
MA.8.G.2.4 Validate and apply Pythagorean Theorem to find distances in real world situations or between points in the coordinate plane.
Find a Missing Length
Write an equation you could use to find the length of the missing side of the right triangle. Then find the missing length. Round to the nearest tenth if necessary.
a2 + b2 = c2 Pythagorean Theorem
122 + 162 = c2 Replace a with 12 and b with 16.
144 + 256 = c2 Evaluate 122 and 162.
400 = c2 Add 144 and 256.
Find a Missing Length
Answer: So, the hypotenuse is 20 inches long.
Definition of square root
c = 20 or –20 Simplify.
The equation has two solutions, 20 and –20. However, the length of a side must be positive.
A. 18 + 9 = c; c = 27 cm
B. 182 + 92 = c2; c = 20.1 cm
C. 182 – 92 = c; c = 243 cm
D. 182 – 92 = c2; c = 15.6 cm
Write an equation you could use to find the length of the missing side of the right triangle. Then find the missing length. Round to the nearest tenth if necessary.
Write an equation you could use to find the length of the missing side of the right triangle. Then find the missing length. Round to the nearest tenth if necessary.
Find a Missing Length
a2 + b2 = c2 Pythagorean Theorem
a2 + 282 = 332 Replace b with 28 and c with 33.
a2 + 784 = 1,089 Evaluate 282 and 332.
Find a Missing Length
a2 + 784 – 784 = 1,089 – 784 Subtract 784 from each side.
a2 = 305 Simplify.
Definition of square root
a 17.5 or –17.5 Use a calculator.
Answer: The length of side a is about 17.5 centimeters.
A. 12 + b2 = 37; 5 ft
B. 12 + b = 37; 25 ft
C. 12 + b2 = 372; 36.8 ft
D. 122 + b2 = 372; 35 ft
Write an equation you could use to find the length of the missing side of the right triangle. Then find the missing length. Round to the nearest tenth if necessary.
Identify a Right Triangle
The measures of three sides of a triangle are 24 inches, 7 inches, and 25 inches. Determine whether the triangle is a right triangle.
a2 + b2 = c2 Pythagorean Theorem
242 + 72 = 252 a = 24, b = 7, c = 25
576 + 49 = 625 Evaluate 242, 72, and 252.
625 = 625 Simplify.
Answer: The triangle is a right triangle.
A. yes
B. no
The measures of three sides of a triangle are 10 centimeters, 12 centimeters, and 14 centimeters. Determine whether the triangle is a right triangle.
A. 3 + 4 = x; 7 cm
B. 32 + 42 = x; 25 cm
C. 32 + 42 = x2; 5 cm
D. 42 – 32 = x2; 1 cm
Write an equation you could use to find the length of the missing side of the right triangle. Then find the missing length.
A. 15 + x = 25; 10 ft
B. 152 + x = 252; 400 ft
C. 15 + x2 = 25; 3.1 ft
D. 152 + x2 = 252; 20 ft
Write an equation you could use to find the length of the missing side of the right triangle. Then find the missing length.
A. x + 12 = 13; 1 in.
B. x2 + 122 = 132; 5 in.
C. x + 122 = 132; 25 in.
D. x2 – 122 = 132; 17.7 in.
Write an equation you could use to find the length of the missing side of the right triangle. Then find the missing length.
A. yes
B. no
C. cannot be determined
Is a triangle with side lengths of 18, 25, and 33 a right triangle?
A. 12 mi
B. 33 mi
C. 35 mi
D. 50 mi
A man drives 33 miles east and 12 miles south. What is the shortest distance between the man and his starting point?
