Question 1: An equilateral triangle has sides of length 6 cm. Calculate its interior angles.

Answer: 60

Question 2: Construct an equilateral triangle with each side measuring 8 cm on the grid.

Answer: Constructed diagram on grid

Question 3: In an equilateral triangle, if one side is increased to 10 cm, what are the new interior angles?

Answer: 60

Question 4: Calculate the height of an equilateral triangle with side length 12 cm.

Answer: 6√3

Question 5: A triangle has two sides of 8 cm each, and the included angle between them is 60°. Is the triangle equilateral? Explain your reasoning.

Answer: No, because the third side would not be 8 cm; using the Law of Cosines, the third side is 8√3 ≈ 13.86 cm, so it's not equilateral.

Question 6: Plot an equilateral triangle with side length 5 units on the grid. Mark all sides and angles.

Answer: Constructed diagram on grid

Question 7: In an equilateral triangle, if one side is decreased to 4 cm, what is the measure of each interior angle?

Answer: 60

Question 8: Calculate the area of an equilateral triangle with side length 10 cm.

Answer: 25√3

Question 9: A student claims that all triangles with angles measuring 60° are equilateral. Is this true? Justify your answer.

Answer: No, because a triangle can have three 60° angles and be isosceles but not necessarily have equal sides; only equilateral triangles have all sides equal.

Question 10: Identify and correct the mistake in this reasoning: 'Since all angles are 60°, the triangle must be equilateral, so all sides are equal.'

Answer: The reasoning is correct; a triangle with all angles of 60° is necessarily equilateral.

Question 11: Challenge: Derive a formula for the height of an equilateral triangle in terms of its side length, and verify it for a side of 14 cm.

Answer: Height = (√3/2) × side; for 14 cm, height = 7√3 cm