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

Answer: 60

Question 2: Calculate the sum of the interior angles of an equilateral triangle.

Answer: 180

Question 3: In an equilateral triangle, if one side is 8 cm, what is the length of each side?

Answer: 8

Question 4: Construct an equilateral triangle with sides measuring 5 cm on the grid. Label the sides.

Answer: See full answer key

Question 5: Explain why all angles in an equilateral triangle are equal.

Answer: Because all sides are equal, the triangle is equilateral, and by the properties of equilateral triangles, all angles are equal, each measuring 60°.

Question 6: A triangle has angles measuring 60°, 60°, and an unknown angle. Is it necessarily equilateral? Explain your reasoning.

Answer: No. It only shows two angles are 60°, but the third could be different unless all three are 60°. For it to be equilateral, all sides and angles must be equal.

Question 7: A student mistakenly claims that in an equilateral triangle, the sides are twice as long as the height. Is this correct? Justify your answer.

Answer: No. In an equilateral triangle with side length s, the height is (√3/2)s, which is not double the side length but about 0.866 times s.

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

Answer: 5√3

Question 9: Plot the graph of y = 2x on the grid. Draw an equilateral triangle with side length 4 units aligned along the graph.

Answer: See full answer key

Question 10: A regular hexagon is made by dividing it into 6 equilateral triangles. What is the measure of each interior angle of these triangles?

Answer: 60

Question 11: Identify and correct the mistake in this statement: 'All equilateral triangles have angles measuring 45 degrees.'

Answer: Incorrect. All angles in an equilateral triangle measure 60°, not 45°.

Question 12: Challenge: Derive a formula for the area of an equilateral triangle in terms of its side length s.

Answer: Area = (√3/4) × s²