Pythagorean Theorem Review

Front

What is the Pythagorean Theorem?

Back

The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). It can be expressed as: a² + b² = c².

Front

How do you determine if a triangle is a right triangle using the Pythagorean Theorem?

Back

To determine if a triangle is a right triangle, check if the squares of the lengths of the two shorter sides add up to the square of the length of the longest side. If a² + b² = c², then the triangle is a right triangle.

Front

What is the height of a pole if a 9 ft wire is stretched from the top to a point 5 ft from the base?

Back

Using the Pythagorean Theorem: h² + 5² = 9²; h² + 25 = 81; h² = 56; h = √56 ≈ 7.5 ft.

Front

What type of triangle has sides of lengths 8.9, 9.2, and 11.3?

Back

The triangle is acute because the square of the longest side (11.3²) is greater than the sum of the squares of the other two sides (8.9² + 9.2²).

Front

What type of triangle has sides of lengths 40, 9, and 41?

Back

The triangle is right because 40² + 9² = 41² (1600 + 81 = 1681).

Front

What type of triangle has sides of lengths 35, 42, and 56?

Back

The triangle is obtuse because the square of the longest side (56²) is greater than the sum of the squares of the other two sides (35² + 42²).

Front

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

Back

It is a right triangle because 5² + 12² = 13² (25 + 144 = 169).

Front

What is the formula to find the distance between two points in a right triangle?

Back

The distance can be found using the Pythagorean Theorem: a² + b² = c², where 'c' is the distance.

Front

What is the relationship between the sides of an obtuse triangle?

Back

In an obtuse triangle, the square of the longest side is greater than the sum of the squares of the other two sides.

Front

What is the relationship between the sides of an acute triangle?

Back

In an acute triangle, the square of the longest side is less than the sum of the squares of the other two sides.