Legs with the 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 type of triangle does the Pythagorean Theorem apply to?

Back

The Pythagorean Theorem ONLY works on right triangles.

Front

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

Back

5m (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 hypotenuse in a right triangle?

Back

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

Front

If the hypotenuse is 10m and one leg is 6m, what is the length of the other leg?

Back

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

Front

What is the relationship between the sides of a right triangle?

Back

In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides.

Front

Can the Pythagorean Theorem be used for non-right triangles?

Back

No, the Pythagorean Theorem is specific to right triangles.

Front

What is an example of a real-world application of the Pythagorean Theorem?

Back

Finding the height of a tree using the distance from the tree and the length of the shadow.

Front

If a ladder is leaning against a wall, how can the Pythagorean Theorem help?

Back

It can help find the distance from the wall to the base of the ladder, using the height it reaches on the wall and the length of the ladder.