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). Formula: a² + b² = c².

Front

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

Back

An obtuse triangle.

Front

What type of triangle has one angle equal to 90 degrees?

Back

A right triangle.

Front

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

Back

An acute triangle.

Front

What is the formula for finding the hypotenuse in a right triangle?

Back

The formula is a² + b² = c².

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

What is the value of x in a right triangle if one leg is 9 and the other leg is 12?

Back

x = 15 (using the Pythagorean theorem: 9² + 12² = x²).

Front

What is a special right triangle?

Back

A special right triangle is a triangle with specific angle measures, such as 45-45-90 or 30-60-90, which have known side ratios.

Front

What are the side ratios of a 45-45-90 triangle?

Back

In a 45-45-90 triangle, the sides are in the ratio 1:1:√2.

Front

What are the side ratios of a 30-60-90 triangle?

Back

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