Pythagorean Theorem and Special Right Triangles

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

What type of triangle has all angles less than 90 degrees?

Back

An acute triangle.

Front

What type of triangle has one angle greater than 90 degrees?

Back

An obtuse triangle.

Front

What is a right triangle?

Back

A right triangle is a triangle that has one angle measuring exactly 90 degrees.

Front

Which set of sides forms a right triangle? 4,5,6 or 5,12,13?

Back

5,12,13 forms a right triangle.

Front

If a triangle has sides of lengths 12, 16, and 20, what type of triangle is it?

Back

It is an obtuse triangle.

Front

What is the value of y in a 45-45-90 triangle if one leg is 9?

Back

y = 9√2.

Front

What is the value of y in a 30-60-90 triangle if the shorter leg is 8?

Back

y = 8√3.

Front

What is the relationship between the sides of a 30-60-90 triangle?

Back

In a 30-60-90 triangle, the lengths of the sides are in the ratio 1:√3:2.

Front

What is the relationship between the sides of a 45-45-90 triangle?

Back

In a 45-45-90 triangle, the lengths of the legs are equal, and the hypotenuse is √2 times the length of a leg.