Pythagorean Theorem REVIEW

Jared needs to create a right triangle to add support to the side of this farm. He buys 3 pieces of wood of length 8 ft, 11 ft, and 15 ft. Did Jared pick the correct sizes in order to create a right triangle, and why?

A triangle PQR is formed by arranging three squares as shown. If triangle PQR is a right triangle, which statement must be true?

• area of square Z = area of square X + area of square Y

• area of square X = area of square Y + area of square Z

• perimeter of square Z = perimeter of square X + perimeter of square Y

• perimeter of square X = perimeter of square Y + perimeter of square Z

Which could be the side lengths of a right triangle?

• 30 cm, 60 cm, 90 cm

• 45 cm, 45 cm, 90 cm

• 52 cm, 165 cm, 173 cm

• 58 cm, 62 cm, 189 cm

Which could be the side lengths of a right triangle? Select ALL that apply.

• 30cm, 60cm, 90cm

• 45cm, 45cm, 90cm

• 52cm, 165cm, 173cm

• 58cm, 62cm, 189cm

• 68cm, 285cm, 293cm

Which student lists three lengths that could represent the sides of a right triangle?

• Galen

• Denise

• Payton

• Wesley

Which is not a right triangle?

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• 
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Baldwin draws a triangle on his paper with the dimensions shown. He would like to know if this is a right triangle. How can he make that determination?

• He can add the two shorter sides, and if their sum is equal to the longest side, the triangle is a right triangle.

• He can add the three sides together, and if they equal 180, the triangle is a right triangle.

• He can find the sum of the squares of the two shorter sides, and if that sum equals the square of the longest side, the triangle is a right triangle.

• He can find the sum of the squares of the longest and middle-length sides, and if that sum is equal to the square of the shortest side, the triangle is a right triangle.

Three friends are playing with wooden dowels of different lengths. Each has a set of 3 dowels.

Marissa's dowels measure 5 inches, 12 inches, and 13 inches.

Berta's dowels measure 6 inches, 8 inches, and 10 inches.

Corrin's dowels measure 12 inches, 16 inches, and 20 inches.

Of the three friends, who can make a right triangle with their dowels, and how do you know?

• All three can make right triangles, because the sums of the squares of the two smaller lengths for each set equals the square of the longest length.

The distance from Tania's house to Julie's house is 1.2 miles. The distance from Julie's house to Natalie's house is 2.4 miles. The distance from Natalie's house to Tania's house is 1.9 miles. Do the three houses form a right triangle? Why or why not?

The location of a public library is 12 km east of a residential apartment. The location of a school is 5 km south of the residential apartment. What is the shortest distance between the public library and the school?

• 7 km

• 11 km

• 13 km

• 17 km