Question 1: What is the measure of each internal angle in an equilateral triangle?

Answer: 60

Question 2: Calculate the length of each side of an equilateral triangle if the height is 6 cm.

Answer: 6√3

Question 3: Construct an equilateral triangle with each side measuring 8 cm on the grid.

Answer: Completed equilateral triangle with sides 8 cm each

Question 4: In an equilateral triangle, if one side is increased by 2 cm, does the triangle remain equilateral? Explain.

Answer: No, all sides must be equal in an equilateral triangle, so increasing one side breaks the property.

Question 5: Find the perimeter of an equilateral triangle with side length 5√2 cm.

Answer: 15√2

Question 6: Explain why all angles in an equilateral triangle are equal, using properties of triangles.

Answer: In an equilateral triangle, all sides are equal, and the angles opposite equal sides are equal. Since the sum of angles is 180°, each angle must be 60°.

Question 7: Plot an equilateral triangle with side length 6 units on the grid.

Answer: Constructed triangle with 6-unit sides

Question 8: A farmer wants to fence a rectangular plot with an equilateral triangle boundary at each corner, each side measuring 10 meters. Calculate the total fence length needed.

Answer: Fencing = 4 × 10 m = 40 m

Question 9: If the side of an equilateral triangle is decreased by 2 cm, what is the new side length if the original was 10 cm? How does this change the area?

Answer: New side = 8 cm; area decreases proportionally

Question 10: Identify the common mistake students make when calculating angles of an equilateral triangle and explain how to avoid it.

Answer: Common mistake: assuming angles are 45° or other incorrect values. To avoid it, remember each angle in an equilateral triangle is 60° because all sides are equal and the sum of interior angles is 180°.

Question 11: Challenge: Prove that the sum of the internal angles of any equilateral triangle is 180° using the properties of isosceles triangles.

Answer: In an equilateral triangle, all sides are equal, so all angles are equal. Each angle = 180°/3 = 60°. Alternatively, draw an altitude, which bisects the angle and forms two 30° angles, confirming the sum is 180°.