9.1 Flashcardizz - 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 can you determine if a triangle is a right triangle using the Pythagorean Theorem?

Back

To determine if a triangle is a right triangle, check if the squares of the lengths of the two shorter sides add up to the square of the length of the longest side. If a² + b² = c², then the triangle is 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

If a triangle has sides of lengths 7, 24, and 25, is it a right triangle?

Back

Yes, because 7² + 24² = 49 + 576 = 625, and 25² = 625.

Front

Solve for x: If one side is 8 and the other side is 15, what is the hypotenuse?

Back

x = 17 (using the Pythagorean Theorem: 8² + 15² = x², 64 + 225 = x², 289 = x², x = 17).

Front

Solve for x: If one side is 12 and the hypotenuse is 13, what is the other side?

Back

x = 5 (using the Pythagorean Theorem: 12² + x² = 13², 144 + x² = 169, x² = 25, x = 5).

Front

What is the relationship between the sides of an obtuse triangle?

Back

In an obtuse triangle, the square of the length of the longest side is greater than the sum of the squares of the lengths of the other two sides.

Front

If a triangle has sides of lengths 9, 12, and 15, is it a right triangle?

Back

No, because 9² + 12² = 81 + 144 = 225, and 15² = 225, so it is a right triangle.

Front

What is the formula to find the area of a right triangle?

Back

The area of a right triangle can be calculated using the formula: Area = (1/2) * base * height.