Pythagorean Theorem Solving/Graphs

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

What are the conditions for a triangle to be a right triangle?

Back

A triangle is a right triangle if one of its angles measures 90 degrees. This can be verified using the Pythagorean Theorem.

Front

If a triangle has sides of lengths 3 in, 4 in, and 5 in, does it form a right triangle?

Back

Yes, because 3² + 4² = 9 + 16 = 25, which is equal to 5².

Front

What is the length of the hypotenuse if the other two sides are 6 in and 8 in?

Back

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

Front

Can the lengths 5, 12, and 13 form a right triangle?

Back

Yes, because 5² + 12² = 25 + 144 = 169, which is equal to 13².

Front

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

Back

The formula is derived from the Pythagorean Theorem: a² + b² = c², where c is the hypotenuse.

Front

If one side of a right triangle is 9 in and the hypotenuse is 15 in, what is the length of the other side?

Back

Using the Pythagorean Theorem: b = √(15² - 9²) = √(225 - 81) = √144 = 12 in.

Front

What is the relationship between the sides of a 30-60-90 triangle?

Back

In a 30-60-90 triangle, the lengths of the sides are in the ratio 1:√3:2.

Front

What is the relationship between the sides of a 45-45-90 triangle?

Back

In a 45-45-90 triangle, the lengths of the legs are equal, and the hypotenuse is √2 times the length of each leg.

Front

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

Back

The triangle inequality theorem states that the sum of the lengths of any two sides must be greater than the length of the third side.