Pythagorean Theorem PRACTICE

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 can you determine if three sides can form a right triangle?

Back

To determine if three sides can form a right triangle, check if the square of the longest side is equal to the sum of the squares of the other two sides (a² + b² = c²).

Front

If the sides are 15 cm, 8 cm, and 17 cm, do they form a right triangle?

Back

Yes, because 15² + 8² = 17² (225 + 64 = 289).

Front

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

Back

To find the missing side, use the Pythagorean Theorem: a² + b² = c², where c is the hypotenuse.

Front

If one side is 8 m and the hypotenuse is 10 m, what is the length of the other side?

Back

Using the Pythagorean Theorem: 8² + b² = 10²; 64 + b² = 100; b² = 36; b = 6 m.

Front

What does it mean if the sides 20 m, 8 m, and 19 m do not form a right triangle?

Back

It means that the relationship a² + b² = c² does not hold true for these sides.

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 a triangle has sides of lengths 5, 12, and 13, does it satisfy the Pythagorean Theorem?

Back

Yes, because 5² + 12² = 13² (25 + 144 = 169).

Front

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

Back

The Pythagorean Theorem is used in various fields such as construction, navigation, and physics to calculate distances and angles.