Understanding the Pythagorean Theorem and Triangle Properties

The video tutorial covers the Pythagorean Theorem, demonstrating how to solve for the hypotenuse and a missing leg in right triangles. It also explains how to calculate the area of a right triangle and an isosceles triangle using the altitude. The tutorial concludes with a discussion on triangle inequality and how to determine if a triangle is right, obtuse, or acute based on side lengths.

What is the length of the hypotenuse in a right triangle with legs measuring 5 and 12?

• 13

• 12

• 10

• 15

How do you calculate the area of a right triangle with base 5 and height 12?

• 25 square units

• 30 square units

• 60 square units

• 120 square units

If a right triangle has a hypotenuse of 10 and one leg of 4, what is the length of the other leg?

• 10

• 6

• 8

• 9

What is the simplified radical form of the square root of 84?

• 3√28

• 2√21

• 4√21

• 5√16

What is the decimal approximation of the square root of 84?

• 8.17

• 9.17

• 11.17

• 10.17

In an isosceles triangle with two sides of 10 and a base of 12, what is the height?

• 8

• 7

• 9

• 6

What is the area of an isosceles triangle with a base of 12 and height of 8?

• 48 square units

• 36 square units

• 24 square units

• 60 square units

What type of triangle is formed if the square of the longest side is equal to the sum of the squares of the other two sides?

• Acute

• Right

• Obtuse

• Scalene

If the square of the longest side is greater than the sum of the squares of the other two sides, what type of triangle is it?

• Obtuse

• Acute

• Equilateral

• Right

What type of triangle is it if the square of the longest side is less than the sum of the squares of the other two sides?

• Obtuse

• Right

• Acute

• Isosceles