lesson menu main idea and new vocabulary ngsss key concept:pythagorean theorem example 1:find a...

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?