Pythagorean/Triangle Inequality Theorem Flashcard

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: c² = a² + b².

Front

What is the Triangle Inequality Theorem?

Back

The Triangle Inequality Theorem states that for any triangle, the sum of the lengths of any two sides must be greater than the length of the third side.

Front

If a triangle has sides of lengths 3, 4, and 5, is it a right triangle?

Back

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

Front

What is the length of the diagonal of a rectangle with width 50 yards and length 100 yards?

Back

The length of the diagonal can be found using the Pythagorean Theorem: d = √(50² + 100²) = √(2500 + 10000) = √12500 = 111.8 yards.

Front

What must be true about the lengths of the sides of a triangle?

Back

The sum of the lengths of any two sides must be greater than the length of the third side.

Front

In a right triangle, which side is the longest?

Back

The hypotenuse is always the longest side in a right triangle.

Front

Can the side lengths 3, 5, and 8 form a triangle?

Back

No, because 3 + 5 is not greater than 8.

Front

What is the relationship between the sides of a triangle if the longest side is 10?

Back

The sum of the lengths of the other two sides must be greater than 10.

Front

If one side of a right triangle is 6 and the other is 8, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: c = √(6² + 8²) = √(36 + 64) = √100 = 10.

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.