Block 4/25-26 - Pythagorean Theorem and Special 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: c² = a² + b².

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 length of the hypotenuse is √2 times the length of a leg.

Front

How do you find the hypotenuse in a 30-60-90 triangle?

Back

In a 30-60-90 triangle, the length of the hypotenuse is twice the length of the shorter leg (30° side), and the longer leg (60° side) is √3 times the length of the shorter leg.

Front

If one leg of a 45-45-90 triangle is 4, what is the length of the hypotenuse?

Back

The hypotenuse is 4√2.

Front

What is the distance formula derived from the Pythagorean Theorem?

Back

The distance between two points (x1, y1) and (x2, y2) in a coordinate plane is given by: d = √((x2 - x1)² + (y2 - y1)²).

Front

In a right triangle, if one leg is 6 and the other leg is 8, what is the length of the hypotenuse?

Back

The hypotenuse is 10, calculated using the Pythagorean Theorem: 10² = 6² + 8².

Front

What is the relationship between the angles in a 45-45-90 triangle?

Back

Both angles are 45 degrees, making it an isosceles right triangle.

Front

How do you calculate the diagonal of a rectangle using the Pythagorean Theorem?

Back

The diagonal (d) can be calculated using the formula: d = √(length² + width²).

Front

If the hypotenuse of a 30-60-90 triangle is 12, what is the length of the shorter leg?

Back

The shorter leg is 6, as it is half the length of the hypotenuse.

Front

What is the value of y in a right triangle if the legs are 5 and 12?

Back

y (the hypotenuse) is 13, calculated using the Pythagorean Theorem: 13² = 5² + 12².