I3 - Pythagorean Theorem

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 do you identify a right triangle using side lengths?

Back

A triangle is a right triangle if the square of the length of the longest side (hypotenuse) is equal to the sum of the squares of the lengths of the other two sides. This can be checked using the Pythagorean Theorem.

Front

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

Back

To find a missing side in a right triangle, use the Pythagorean Theorem: a² + b² = c², where c is the hypotenuse and a and b are the other two sides.

Front

If one side of a right triangle is 15 and the hypotenuse is 21, what is the length of the other side?

Back

Using the Pythagorean Theorem: 15² + x² = 21². Solving gives x = 18.

Front

What are the conditions for a triangle to be classified as acute, obtuse, or right?

Back

A triangle is acute if a² + b² > c², obtuse if a² + b² < c², and right if a² + b² = c², where c is the longest side.

Front

What is the relationship between the sides of a 5-12-13 triangle?

Back

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

Front

How do you round a number to the nearest tenth?

Back

To round a number to the nearest tenth, look at the hundredths place. If it is 5 or greater, round up the tenths place by one. If it is less than 5, keep the tenths place the same.

Front

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

Back

The hypotenuse is the longest side of a right triangle and is opposite the right angle. It is crucial for applying the Pythagorean Theorem.

Front

What is the value of x in the equation x² + 14² = 20²?

Back

Using the Pythagorean Theorem: x² + 196 = 400. Solving gives x = 12.

Front

What does it mean for a triangle to be obtuse?

Back

An obtuse triangle has one angle that is greater than 90 degrees. The relationship between its sides is a² + b² < c², where c is the longest side.