Properties and Formulas of Triangles

The video tutorial explains the unique properties of equilateral triangles, where all sides and angles are equal. It discusses how dropping a perpendicular from a vertex divides the opposite side into two equal parts, a concept applicable to isosceles triangles as well. The tutorial then derives the formula for the area of an equilateral triangle using the Pythagorean theorem, expressing the area in terms of the side length. Finally, it demonstrates how to apply this formula to calculate the area, emphasizing the importance of understanding the derivation for quick recall.

What is a unique property of an equilateral triangle?

• Only two sides are equal.

• All angles are different.

• All sides and angles are equal.

• All sides are different.

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

• Only one side is equal to the base.

• All sides are equal.

• Two sides are equal.

• No sides are equal.

If each angle in an equilateral triangle is X, what is the value of X?

• 90°

• 60°

• 120°

• 45°

What is the sum of all angles in any triangle?

• 90°

• 360°

• 270°

• 180°

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

• 45°

• 60°

• 90°

• 120°

What happens when a perpendicular is dropped from a vertex in an equilateral triangle?

• It divides the opposite side into two unequal parts.

• It divides the opposite side into two equal parts.

• It does not intersect the opposite side.

• It forms a right angle with the base.

What does the perpendicular do in an equilateral triangle?

• Does not intersect the base.

• Divides the base into two equal parts.

• Forms an obtuse angle with the base.

• Divides the triangle into two unequal parts.

In an isosceles triangle, what does the perpendicular from the vertex do?

• Forms an obtuse angle with the base.

• Does not intersect the base.

• Divides the base into two equal parts.

• Divides the base into two unequal parts.

What is the base of an equilateral triangle if the side is s?

• 2s

• s

• s/2

• s√3

Which theorem is used to derive the height of an equilateral triangle?

• Cosine Rule

• Sine Rule

• Thales' Theorem

• Pythagorean Theorem