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 can be expressed as: c² = a² + b².

Front

What is the hypotenuse in a right triangle?

Back

The hypotenuse is the longest side of a right triangle, opposite the right angle.

Front

If one leg of a right triangle is 3 and the other leg is 4, what is the length of the hypotenuse?

Back

5 (Using the Pythagorean Theorem: 3² + 4² = 9 + 16 = 25; √25 = 5).

Front

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

Back

To find the length of a missing leg, rearrange the Pythagorean Theorem: a² = c² - b², where c is the hypotenuse and b is the known leg.

Front

What is the area of a square with a side length of 5?

Back

25 cm² (Area = side² = 5²).

Front

If a triangle has a hypotenuse of 10 and one leg of 6, what is the length of the other leg?

Back

8 (Using the Pythagorean Theorem: 10² - 6² = 100 - 36 = 64; √64 = 8).

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 each leg.

Front

If a ladder is leaning against a wall forming a right triangle, how can you find the height it reaches on the wall?

Back

Use the Pythagorean Theorem: height = √(ladder² - distance from wall²).

Front

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

Back

Area = (1/2) × base × height.