Mastering Geometry: Pythagorean Theorem and Beyond

If a right triangle has legs of lengths 6 cm and 8 cm, the length of the hypotenuse is _____.

Which of the following triangles is a special right triangle?

• A triangle with sides 3, 4, 5

• Both A and B

• Neither A nor B

The distance between the points (3, 4) and (7, 1) is (a)   .

• 5 units
• 4 units

The midpoint of the line segment connecting the points (2, 3) and (4, -1) is _____.

Which of the following statements is true for the converse of the Pythagorean theorem?

• If the square of the longest side of a triangle equals the sum of the squares of the other two sides, then the triangle is a right triangle.

• If the square of the longest side of a triangle is less than the sum of the squares of the other two sides, then the triangle is a right triangle.

• If the square of the longest side of a triangle is more than the sum of the squares of the other two sides, then the triangle is a right triangle.

• None of the above.

A triangle has sides of lengths 5, 12, and 13. It is (a)   .

• It is a right triangle.
• It is an obtuse triangle.
• It is an acute triangle.
• It is not a triangle.

The length of the hypotenuse of a right triangle if one leg is 7 units long and the other leg is 24 units long is _____.

In a 45°-45°-90° triangle, if one leg is 8 cm long, how long is the hypotenuse?

• 16 cm

• 8 cm

Calculate the distance between the points (-3, -2) and (1, 2).

• 5 units

• 6 units

What is the midpoint of the line segment connecting the points (-4, 5) and (2, 9)?

• (-1, 7)

• (-2, 7)

• (-1, 8)

• (1, 7)