Pythagorean Theorem & Converse

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 a triangle is acute, obtuse, or right using side lengths?

Back

To determine the type of triangle using side lengths, compare the square of the longest side (c) to the sum of the squares of the other two sides (a and b): - If a² + b² > c², the triangle is acute. - If a² + b² = c², the triangle is right. - If a² + b² < c², the triangle is obtuse.

Front

What is the definition of a hypotenuse in a right triangle?

Back

The hypotenuse is the longest side of a right triangle, opposite the right angle.

Front

Given the sides of a triangle as 4, 5, and 6, what type of triangle is it?

Back

The triangle with sides 4, 5, and 6 is an acute triangle.

Front

What is the length of the hypotenuse if the legs of a right triangle are 10 and 24?

Back

The length of the hypotenuse is 26, calculated using the Pythagorean Theorem: 10² + 24² = 100 + 576 = 676, and √676 = 26.

Front

If a triangle has sides 11, 12, and 15, what type of triangle is it?

Back

The triangle with sides 11, 12, and 15 is an acute triangle.

Front

What is the relationship between the sides of a right triangle?

Back

In a right triangle, the relationship between the sides is defined by the Pythagorean Theorem: a² + b² = c², where c is the hypotenuse.

Front

How do you find the length of a side in a right triangle if you know the other two sides?

Back

To find the length of a side in a right triangle, use the Pythagorean Theorem. Rearrange the formula to solve for the unknown side: - If finding the hypotenuse: c = √(a² + b²) - If finding a leg: a = √(c² - b²) or b = √(c² - a²).

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.