Pythagorean Theorem and Their Converse

If the sides of a triangle are 7, 24, and 25, is it a right triangle?

• Yes, it is a right triangle because 7² + 24² = 25².

• No, it is not a right triangle because the sides do not satisfy the Pythagorean theorem.

• Yes, it is a right triangle because 7² + 25² = 24².

• No, it is not a right triangle because the longest side is not the hypotenuse.

Tags

CCSS.8.G.B.8

If a triangle has sides of lengths 5, 12, and 13, is it a right triangle?

• Yes, because 5² + 12² = 13².

• No, because the sides do not satisfy the Pythagorean theorem.

• Yes, but only if the triangle is isosceles.

• No, because the longest side is not the hypotenuse.

Tags

CCSS.8.G.B.8

a = 2.1, b = 7.2, c = 7.5. Is this a right triangle?

• Yes, it is a right triangle because 2.1² + 7.2² = 7.5².

• No, it is not a right triangle because 2.1 + 7.2 ≠ 7.5.

• Yes, it is a right triangle because 2.1 + 7.2 = 7.5.

• No, it is not a right triangle because 2.1² + 7.5² = 7.2².

Tags

CCSS.8.G.B.8

If a triangle has sides 9, 12, and 15, is it a right triangle?

• Yes, because 9² + 12² = 15².

• No, because 9² + 12² ≠ 15².

• Yes, because it follows the Pythagorean theorem.

• No, because the longest side is not the hypotenuse.

Tags

CCSS.8.G.B.8

What is the hypotenuse in a right triangle?

• The side opposite the right angle, and the longest side.

• The side adjacent to the right angle.

• The shortest side of the triangle.

• The side opposite the smallest angle.

What does the Pythagorean theorem state?

• In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

• The sum of the angles in a triangle is always 180 degrees.

• In any triangle, the longest side is always opposite the largest angle.

• The area of a circle is equal to π times the radius squared.

Tags

CCSS.8.G.B.8

What are the legs of a right triangle?

• The two sides that form the right angle.

• The longest side of the triangle.

• The two sides opposite the right angle.

• The two sides that are equal in length.

Can a triangle with sides 8, 15, and 17 be a right triangle?

• Yes, because 8² + 15² = 17².

• No, because the sides do not satisfy the Pythagorean theorem.

• Yes, but only if the triangle is isosceles.

• No, because the longest side must be the hypotenuse.

Tags

CCSS.8.G.B.8

What is the longest side of a right triangle called?

• Base

• Altitude

• Hypotenuse

• Leg

What is the Pythagorean theorem used for?

• To determine if a triangle is a right triangle and to find the length of a side.

• To calculate the area of a triangle.

• To find the circumference of a circle.

• To determine the angles of a triangle.

Tags

CCSS.8.G.B.8