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 does the Pythagorean Theorem apply to?

Back

The Pythagorean Theorem ONLY works on right triangles.

Front

What are the side lengths 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. The shortest side is opposite the 30° angle, the longer leg is opposite the 60° angle, and the hypotenuse is opposite the right angle.

Front

What are the side lengths 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 each leg.

Front

How do you find the length of the diagonal of a rectangle?

Back

Use the Pythagorean Theorem. If the rectangle has width (w) and length (l), the diagonal (d) can be found using the formula: d = √(w² + l²).

Front

What is an obtuse triangle?

Back

An obtuse triangle is a triangle that has one angle greater than 90 degrees.

Front

What is an acute triangle?

Back

An acute triangle is a triangle where all three angles are less than 90 degrees.

Front

What is a right triangle?

Back

A right triangle is a triangle that has one angle equal to 90 degrees.

Front

Can a triangle have side lengths of 4, 5, and 9?

Back

No, these lengths do not satisfy the triangle inequality theorem, which states that the sum of the lengths of any two sides must be greater than the length of the third side.

Front

What is the formula to determine if a triangle is right, acute, or obtuse?

Back

For a triangle with sides a, b, and c (where c is the longest side): If a² + b² = c², it's a right triangle; if a² + b² > c², it's acute; if a² + b² < c², it's obtuse.