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: a² + b² = c².

Front

What is a right triangle?

Back

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

Front

How do you identify the hypotenuse in a right triangle?

Back

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

Front

If a triangle has sides measuring 3 cm, 4 cm, and 5 cm, is it a right triangle?

Back

Yes, it is a right triangle because 3² + 4² = 5² (9 + 16 = 25).

Front

What is the formula to find the length of the missing side in a right triangle?

Back

Use the Pythagorean Theorem: a² + b² = c², where c is the hypotenuse.

Front

If a boat sails 6 miles north and 8 miles east, how far is it from its original location?

Back

10 miles, calculated using the Pythagorean Theorem: 6² + 8² = 10² (36 + 64 = 100).

Front

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

Back

It means that one of its angles is exactly 90 degrees.

Front

Can a triangle with sides measuring 4 in, 5 in, and 6 in be a right triangle?

Back

No, it is not a right triangle because 4² + 5² ≠ 6² (16 + 25 ≠ 36).

Front

What is the significance of the Pythagorean Theorem in real life?

Back

It is used in various fields such as construction, navigation, and physics to determine distances and relationships between sides.

Front

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

Back

In a right triangle, the sum of the squares of the two shorter sides equals the square of the longest side (hypotenuse).