Pythagorean Theorem Review

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

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

Back

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

Front

What is the distance formula derived from the Pythagorean Theorem?

Back

The distance between two points (x1, y1) and (x2, y2) in a coordinate plane is given by: d = √((x2 - x1)² + (y2 - y1)²).

Front

In a right triangle, if the lengths of the two legs are equal, what type of triangle is it?

Back

It is an isosceles right triangle.

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

Back

8 units (Using the Pythagorean Theorem: 6² + b² = 10²; 36 + b² = 100; b² = 64; b = 8).

Front

What is the area of a right triangle with legs of length 5 units and 12 units?

Back

30 square units (Area = 1/2 * base * height = 1/2 * 5 * 12).

Front

How do you find the length of a side in a right triangle if you know the lengths of the other two sides?

Back

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

Front

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

Back

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