L 7-4 Pythagorean Converse

John is building a wooden frame for his new painting. He cuts three pieces of wood with lengths 3, 4, and 5 feet. Can he form a right triangle with these pieces to ensure the frame is stable?

• Maybe

• Sometimes

• No

• Yes

Answer explanation

The triangle with side lengths 3, 4, 5 is a right triangle because it follows the Pythagorean theorem (3^2 + 4^2 = 5^2), making it a right triangle.

Tags

CCSS.8.G.B.8

Consider a scenario where you're helping a friend construct a ramp for a skateboarding event. To ensure the ramp can be classified as a right-angled ramp, you measure the sides and find them to be 6, 8, and 10 feet respectively. Apply the converse of the Pythagorean theorem to determine if this ramp can indeed be considered a right-angled ramp.

• No, the ramp forms an obtuse triangle

• Yes, the ramp with side lengths 6, 8, 10 feet forms a right-angled triangle.

• No, the ramp does not form a right-angled triangle

• Yes, the ramp with side lengths 6, 8, 10 feet forms an equilateral triangle

Answer explanation

The triangle with side lengths 6, 8, 10 satisfies the Pythagorean theorem (6^2 + 8^2 = 10^2), making it a right triangle.

Tags

CCSS.8.G.B.8

In a triangle with side lengths 5, 12, x, find the value of x if it is a right triangle.

• 10

• 13

• 20

• 15

Answer explanation

In a right triangle, the side lengths satisfy the Pythagorean theorem (a^2 + b^2 = c^2). Therefore, x = sqrt(12^2 + 5^2) = 13.

Tags

CCSS.8.G.B.8

Determine if the triangle with side lengths 9, 12, 15 is a right triangle using the converse of Pythagorean theorem.

• Maybe

• No

• Sometimes

• Yes

Answer explanation

The triangle with side lengths 9, 12, 15 is a right triangle because it satisfies the converse of the Pythagorean theorem, where the square of the longest side (15^2) is equal to the sum of the squares of the other two sides (9^2 + 12^2).

Tags

CCSS.8.G.B.8

Find the missing side length in a right triangle with sides 7, 24, x.

• 15

• 30

• 25

• 20

Answer explanation

In a right triangle, the missing side length can be found using the Pythagorean theorem: a^2 + b^2 = c^2. Therefore, x = sqrt(24^2 + 7^2) = sqrt(625) = 25.

Tags

CCSS.8.G.B.7

Imagine you're helping a friend calculate if the wooden frame they're building for a garden project, with side lengths 13 feet, 84 feet, and 85 feet, forms a right triangle. Would applying the converse of the Pythagorean theorem confirm it's a right triangle?

• Maybe

• No

• Yes

• Not sure

Answer explanation

The triangle with side lengths 13, 84, 85 is a right triangle because it satisfies the Pythagorean theorem's converse, where the square of the longest side (85^2) equals the sum of the squares of the other two sides (13^2 + 84^2).

Tags

CCSS.8.G.B.8

Given a triangle with sides 10, 24, x, calculate the value of x if it is a right triangle.

• 20.1

• 18.24

• 15.5

• 21.82

Answer explanation

In a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. Therefore, x = sqrt(10^2 + 24^2) = 21.82.

Tags

CCSS.8.G.B.8

Check if the triangle with side lengths 15, 20, 25 is a right triangle using the converse of Pythagorean theorem.

• Yes

• No

• Sometimes

• Maybe

Answer explanation

The triangle with side lengths 15, 20, 25 satisfies the converse of Pythagorean theorem (a^2 + b^2 = c^2), making it a right triangle. Therefore, the correct answer is 'Yes'.

Tags

CCSS.8.G.B.8

Imagine you're helping a friend, Alex, build a triangular shelf where two sides are 8 inches and 15 inches long. To ensure the shelf is stable and forms a right angle, how long should the third side, x, be?

• √169

• 10

• 12

• √161

Answer explanation

To determine the missing side of a right triangle, use the Pythagorean theorem. In this case, x = √(15^2 + 8^2) = √(225 + 64) = √289 = √(17^2) = 17.

Tags

CCSS.8.G.B.8

Verify if the triangle with side lengths 17, 144, 145 is a right triangle by applying the converse of Pythagorean theorem.

• No

• Maybe

• Sometimes

• Yes

Answer explanation

The triangle with side lengths 17, 144, 145 satisfies the condition a^2 + b^2 = c^2, confirming it is a right triangle. Therefore, the correct answer is 'Yes'.

Tags

CCSS.8.G.B.8