Pythagorean Theorem Models

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 are the sides of a right triangle?

Back

In a right triangle, the two shorter sides are called the legs (a and b), and the longest side opposite the right angle is called the hypotenuse (c).

Front

If a right triangle has legs of lengths 3 and 4, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: 3² + 4² = c²; 9 + 16 = c²; 25 = c²; c = 5.

Front

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

Back

The area of a square is calculated as side length squared. Therefore, area = 5² = 25 square units.

Front

If the area of square A is 144 cm², what is the length of one side?

Back

To find the side length, take the square root of the area: √144 = 12 cm.

Front

What is the relationship between the areas of squares in a right triangle?

Back

The area of the square on the hypotenuse is equal to the sum of the areas of the squares on the other two sides: Area(c) = Area(a) + Area(b).

Front

If a = 6 and b = 8, what is the area of square c?

Back

Using the Pythagorean Theorem: 6² + 8² = c²; 36 + 64 = c²; 100 = c²; c = 10. Area of square c = 10² = 100.

Front

What does it mean if a triangle is a right triangle?

Back

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

Front

What is the formula to find the area of a triangle?

Back

The area of a triangle can be calculated using the formula: Area = 1/2 * base * height.

Front

If the lengths of the sides of a triangle are 5, 12, and 13, is it a right triangle?

Back

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