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). Formula: c² = a² + b².

Front

What is a right triangle?

Back

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

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 lengths of the two legs of a right triangle are 3 cm and 4 cm, what is the length of the hypotenuse?

Back

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

Front

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

Back

25 cm² (Area = side length × side length).

Front

If the area of square a is 45 in² and the area of square b is 65 in², what is the area of square c?

Back

110 in² (Area of square c = area of square a + area of square b).

Front

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

Back

The sum of the areas of the squares on the two legs equals the area of the square on the hypotenuse.

Front

If the area of the blue square is 25 in² and the area of the green square is 169 in², what is the area of the yellow square?

Back

144 in² (Area of yellow square = area of green square - area of blue square).

Front

What is the formula for the area of a triangle?

Back

Area = 1/2 × base × height.

Front

What does it mean for a triangle to be isosceles?

Back

An isosceles triangle has at least two sides that are equal in length.