Exploring the Pythagorean Theorem in Triangle Applications

The video tutorial introduces the Pythagorean theorem and demonstrates its use in solving problems related to right triangles. It covers finding missing sides, verifying if a triangle is a right triangle, and applying the theorem to a real-world scenario involving distance calculation. The tutorial provides step-by-step explanations and examples to enhance understanding.

What is the Pythagorean theorem formula?

• a^2 + b^2 = c^2

• a^2 * b^2 = c^2

• a^2 - b^2 = c^2

• a^2 + b^2 = 2c

Which side of the triangle is always the hypotenuse?

• The side opposite the right angle

• The side adjacent to the right angle

• The shortest side

• Any side

If a triangle has sides of 5, 12, and 13, is it a right triangle?

• Yes

• No

• Only if it has a right angle

• Insufficient information

How do you find the missing side 'x' in a right triangle if the other sides are known?

• Substitute the known values into the Pythagorean theorem and solve for x

• Add the squares of the known sides

• Multiply the known sides and take the square root

• Subtract the known sides from each other

What is the value of x if the sides of the triangle are 5, x, and 7?

• 2√6

• √24

• √19

• 6

How can you verify if a triangle with sides 4, 5, and 6 is a right triangle?

• Add all the sides and divide by 2

• Check if any angle is 90 degrees

• Measure the angles with a protractor

• Use the Pythagorean theorem to check if the squares of the shorter sides sum up to the square of the longest side

What conclusion can be drawn if the sum of the squares of the two shorter sides is greater than the square of the longest side?

• The triangle is obtuse

• The triangle is acute

• The triangle is right

• The triangle is equilateral

Jack travels 5 feet north and Jill travels 12 feet east. How far apart are they?

• 13 feet

• 12 feet

• 17 feet

• 5 feet

What is a Pythagorean triple?

• A method to determine the height of a triangle

• A formula to calculate the area of a triangle

• A triangle with three equal sides

• A set of three integers that satisfy the Pythagorean theorem

If the distance between two points is calculated using the Pythagorean theorem, what shape is formed by these points and their paths?

• Rectangle

• Square

• Circle

• Right triangle