Apothem and Triangle Properties

The video tutorial explains how to find the length of the apothem in an equilateral triangle. It begins by defining the apothem as the shortest distance from the center to a side of the triangle. The instructor then draws strategic lines, including the radius, to form a right triangle and analyzes the angles involved. Using known side lengths and geometric formulas, the apothem is calculated, demonstrating the process step-by-step.

What is the apothem in an equilateral triangle?

• The angle bisector of the triangle

• The longest side of the triangle

• The shortest distance from the center to a side

• The distance from the center to a vertex

How is the radius related to the apothem in an equilateral triangle?

• The radius is twice the apothem

• The radius is the same as the apothem

• The radius is half the apothem

• The radius is the distance from the center to a vertex

What is the measure of each angle in an equilateral triangle?

• 90 degrees

• 30 degrees

• 45 degrees

• 60 degrees

In the right triangle formed, what is the relationship between the apothem and the angles?

• The apothem is opposite the 60-degree angle

• The apothem is opposite the 90-degree angle

• The apothem is opposite the 30-degree angle

• The apothem is the hypotenuse

If the full side of the equilateral triangle is 6, what is the length of the segment formed by the apothem?

• 3

• 6

• 12

• 9

What is the formula for the sides of a 30-60-90 triangle?

• Short leg is x, hypotenuse is x root 3, long leg is 2x

• Short leg is x, hypotenuse is 2x, long leg is x root 3

• Short leg is x root 3, hypotenuse is x, long leg is 2x

• Short leg is 2x, hypotenuse is x root 3, long leg is x

How do you solve for x in the equation x root 3 = 6?

• Divide both sides by root 3

• Add root 3 to both sides

• Subtract root 3 from both sides

• Multiply both sides by root 3

What is the result of rationalizing the denominator of 6/root 3?

• 2 root 3

• 3 root 6

• 3 root 2

• 6 root 3

What is the final length of the apothem after rationalizing the denominator?

• 3 root 2

• 2 root 3

• 6 root 3

• 3 root 6

Why is it necessary to rationalize the denominator in the final step?

• To simplify the expression

• To make the calculation easier

• To convert it into a whole number

• To ensure the denominator is not a radical