Pythagorean Theorem - basics

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

Back

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

Front

Which set of sides can form a right triangle? 5, 12, 13 or 8, 10, 12?

Back

5, 12, 13 can form a right triangle because 5² + 12² = 13² (25 + 144 = 169).

Front

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

Back

The formula is derived from the Pythagorean Theorem: c² = a² + b², where c is the hypotenuse and a and b are the other two sides.

Front

What does it mean for two triangles to be similar?

Back

Two triangles are similar if their corresponding angles are equal and their corresponding sides are in proportion.

Front

How do you determine if a triangle is a right triangle using side lengths?

Back

You can use the Pythagorean Theorem: if a² + b² = c² holds true for the side lengths, then the triangle is a right triangle.

Front

What is the relationship between the areas of the squares on the sides of 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.

Front

If a triangle has sides of lengths 6, 8, and 10, is it a right triangle?

Back

Yes, because 6² + 8² = 10² (36 + 64 = 100).