Pythagorean Theorem and Converse Warmup

Front

What is the Pythagorean Theorem?

Back

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). Formula: a² + b² = c².

Front

What type of triangle is formed by the sides 6, 9, and 17?

Back

Not a triangle. The sum of the lengths of the two shorter sides (6 + 9 = 15) is less than the length of the longest side (17).

Front

What is the converse of the Pythagorean Theorem?

Back

If a triangle has side lengths a, b, and c, and a² + b² = c², then the triangle is a right triangle.

Front

Which set of sides forms a right triangle: 4, 5, 6 or 5, 12, 13?

Back

5, 12, 13. This set satisfies the Pythagorean Theorem: 5² + 12² = 13².

Front

How do you find the missing side of a right triangle?

Back

Use the Pythagorean Theorem: If you know two sides, you can find the third side by rearranging the formula: c = √(a² + b²) or a = √(c² - b²) or b = √(c² - a²).

Front

What is the value of x if 2x² + 8 = 40?

Back

x = 2√5. Solve for x by isolating x²: 2x² = 32, x² = 16, x = 4.

Front

What is the simplified form of √96?

Back

4√6. Factor 96 into 16 and 6, then take the square root of 16.

Front

What is an acute triangle?

Back

A triangle where all three angles are less than 90 degrees.

Front

What is an obtuse triangle?

Back

A triangle that has one angle greater than 90 degrees.

Front

What is a right triangle?

Back

A triangle that has one angle equal to 90 degrees.