Special Right Triangles (Quiz)

Consider triangle QRS. The legs each have a length of 10 units. What is the length of the hypotenuse of the triangle?

D. 10√2

Consider triangle DEF. The legs have a length of 36 units each. What is the length of the hypotenuse of the triangle

D. 36√2

The length of segment EF is 12 cm. Which statements regarding triangle DEF are correct? Select three options.

~ A. EF is the longest side of △DEF. ~ B. DF = 6 cm ~ E. DE = 6√3 cm

Each leg of a 45°-45°-90° triangle measures 12 cm. What is the length of the hypotenuse?

D. 12√2

Triangle MNO is an equilateral triangle with sides measuring 16√3 units. What is the height of the triangle?

B. 24 units

Consider triangle GHJ. What is the length of line segment HJ?

B. 5√3

A wall in Maria's bedroom is in the shape of a trapezoid. The wall can be divided into a rectangle and a triangle. Using the 45°-45°-90° triangle theorem, find the value of h, the height of the wall.

C. 13ft

The height of trapezoid VWXZ is 8√3 units. The upper base,VW, measures 10 units. Use the 30°-60°-90° triangle theorem to find the length of YX. Once you you know the length of YX, find the length of the lower base, ZX.

C. 18 units

Consider the incomplete paragraph proof. Prove: In a 45°-45°-90° triangle, the hypotenuse is √2 times the length of each leg. Because triangle XYZ is a right triangle, the side lengths must satisfy the Pythagorean theorem, a2 + b2 = c2, which in this isosceles triangle becomes a2 + a2 = c2. By combining like terms, 2a2 = c2. Which final step will prove that the length of the hypotenuse, c, √2 is times the length of each leg?

C. Determine the principal square root of both sides of the equation.

Jules owns a square plot of land that measures 30 yards on each side. He plans to divide the land in half by building a fence, as shown by the dotted line below. How many yards of fencing will Jules need?

NOT B. 30yd