Pythagorean Theorem and Inequality

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

How can you determine if three lengths can form a right triangle?

Back

To determine if three lengths can form a right triangle, check if the square of the longest length equals the sum of the squares of the other two lengths. If a² + b² = c², then they can form a right triangle.

Front

What is an acute triangle?

Back

An acute triangle is a triangle where all three interior angles are less than 90 degrees.

Front

What is an obtuse triangle?

Back

An obtuse triangle is a triangle that has one interior angle greater than 90 degrees.

Front

What is a right triangle?

Back

A right triangle is a triangle that has one interior angle equal to 90 degrees.

Front

Can the lengths 9, 15, and 12 form a right triangle?

Back

Yes, because 9² + 12² = 81 + 144 = 225 = 15².

Front

Can the lengths 8, 10, and 6 form a right triangle?

Back

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

Front

Can the lengths 6, 4, and 12 form a right triangle?

Back

No, because 6² + 4² = 36 + 16 = 52, which is not equal to 12² (144).

Front

How do you identify an obtuse triangle using side lengths?

Back

To identify an obtuse triangle, check if the square of the longest side is greater than the sum of the squares of the other two sides. If c² > a² + b², then it is obtuse.

Front

How do you identify an acute triangle using side lengths?

Back

To identify an acute triangle, check if the square of the longest side is less than the sum of the squares of the other two sides. If c² < a² + b², then it is acute.