Pythagorean Theorem Flashcard

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: c² = a² + b².

Front

If a right triangle has legs of lengths 3 and 4, what is the length of the hypotenuse?

Back

Using the Pythagorean Theorem: c² = 3² + 4² = 9 + 16 = 25. Therefore, c = √25 = 5.

Front

What is the formula to find the perimeter of a triangle?

Back

The perimeter of a triangle is the sum of the lengths of its three sides: P = a + b + c.

Front

In a right triangle, if one leg is 6 and the hypotenuse is 10, what is the length of the other leg?

Back

Using the Pythagorean Theorem: c² = a² + b². Here, 10² = 6² + b², so 100 = 36 + b², thus b² = 64, and b = √64 = 8.

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. The side opposite the 30° angle is the shortest, the side opposite the 60° angle is √3 times the shortest, and the hypotenuse is twice the shortest.

Front

How do you calculate the area of a right triangle?

Back

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

Front

What is the distance formula derived from the Pythagorean Theorem?

Back

The distance between two points (x1, y1) and (x2, y2) in a coordinate plane is given by: d = √((x2 - x1)² + (y2 - y1)²).

Front

If the lengths of the legs of a right triangle are both equal, what type of triangle is it?

Back

It is an isosceles right triangle.

Front

What is the hypotenuse of a right triangle with legs of lengths 8 and 15?

Back

Using the Pythagorean Theorem: c² = 8² + 15² = 64 + 225 = 289. Therefore, c = √289 = 17.

Front

What is the perimeter of a triangle with sides of lengths 5, 12, and 13?

Back

The perimeter is P = 5 + 12 + 13 = 30.