Mastering the Pythagorean Theorem and Diagonal Proof

A right triangle has legs of lengths 6 cm and 8 cm. What is the length of the hypotenuse?

• 10 cm

• 12 cm

• 14 cm

• 16 cm

Tags

CCSS.8.G.B.7

If a square has a side length of 5 cm, what is the length of its diagonal?

• 5 cm

• 7 cm

• 10 cm

Tags

CCSS.8.G.B.8

How can the Pythagorean theorem be used to determine if a triangle with sides of lengths 9, 12, and 15 is a right triangle?

• It cannot be used to determine if it's a right triangle

Tags

CCSS.8.G.B.8

A ladder is leaning against a wall, reaching a height of 12 feet. If the base of the ladder is 5 feet away from the wall, how long is the ladder?

• 13 feet

• 14 feet

• 15 feet

• 17 feet

Tags

CCSS.8.G.B.8

In proving the Pythagorean theorem using algebra, which of the following is a necessary step?

• Demonstrating that the area of a square is equal to the sum of the areas of four right triangles and a smaller square

• Showing that the sum of the angles in a triangle is 180 degrees

• Proving that all triangles are right triangles

• Establishing that the sum of the squares of the legs is equal to the square of the hypotenuse

Tags

CCSS.8.G.B.8

Which of the following figures always contains right triangles?

• Equilateral triangles

• Isosceles triangles

• Squares

• Circles

Tags

CCSS.2.G.A.1

A triangle has one angle of 90 degrees and the lengths of the two legs are 7 cm and 24 cm. What is the length of the hypotenuse?

• 25 cm

• 31 cm

• 17 cm

• 29 cm

Tags

CCSS.8.G.B.7

What is the diagonal length of a rectangle with length 10 cm and width 6 cm?

• 8 cm

• 12 cm

• 16 cm

Tags

CCSS.8.G.B.7

Which of the following is an application of the Pythagorean theorem in real life?

• Calculating the height of a building using a shadow

• Determining the volume of a cylinder

• Measuring the acidity of a solution

• Estimating the growth rate of a population

Tags

CCSS.8.G.B.8

A right triangle has a hypotenuse of length 13 cm and one leg of length 5 cm. What is the length of the other leg?

• 12 cm

Tags

CCSS.8.G.B.7