Pythagorean Theorem

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 is expressed as a² + b² = c².

Front

What is the longest side of a right triangle called?

Back

The longest side of a right triangle is called the hypotenuse.

Front

If a triangle has sides of lengths 7, 11, and 13, what type of triangle is it?

Back

It is an acute triangle because the square of the longest side (13² = 169) is greater than the sum of the squares of the other two sides (7² + 11² = 49 + 121 = 170).

Front

How do you find the length of the hypotenuse in a right triangle?

Back

Use the Pythagorean Theorem: c = √(a² + b²), where c is the hypotenuse and a and b are the other two sides.

Front

What is the value of 'a' if b = 35 and c = 37 in the equation a² + b² = c²?

Back

a = 12, because 12² + 35² = 144 + 1225 = 1369 = 37².

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.

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

If a ladder is placed 10 feet away from a house and needs to reach a height of 25 feet, how tall must the ladder be?

Back

The ladder must be 27 feet tall, calculated using the Pythagorean Theorem: c = √(10² + 25²) = √(100 + 625) = √725 ≈ 26.93.

Front

What does it mean for a triangle to be a right triangle?

Back

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

Front

What is the formula to calculate the area of a right triangle?

Back

The area of a right triangle is given by the formula: Area = (1/2) * base * height.