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

Answer: 60

Question 2: If one side of an equilateral triangle is 8 cm, what is the perimeter?

Answer: 24

Question 3: Construct an equilateral triangle with sides of 5 cm on the grid. Show all steps.

Answer: Students draw and label the triangle, ensuring all sides are equal at 5 cm.

Question 4: Calculate the height of an equilateral triangle with side length 10 cm. Use pythagoras or other methods. Show your working.

Answer: Approx. 8.66 cm

Question 5: A triangle has two sides equal, both measuring 7 cm, and the included angle is 60°. Is this triangle equilateral? Explain your reasoning.

Answer: No, because the third side length depends on the included angle; it is not necessarily 7 cm.

Question 6: A construction problem: On the grid, construct an equilateral triangle with side length 6 cm. Label all sides and angles.

Answer: Students produce a triangle with all sides 6 cm and angles 60°.

Question 7: In an equilateral triangle, if one side is extended by 2 cm, what is the new perimeter? Assume original side is 9 cm.

Answer: 30 cm

Question 8: Explain why all angles in an equilateral triangle are equal. Use mathematical reasoning.

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

Question 9: A student claims that an equilateral triangle can have angles of 50°, 50°, and 80°. Identify and explain the mistake.

Answer: The total angles sum to 180°, but 50° + 50° + 80° = 180°; however, these do not form an equilateral triangle, which must have all angles equal to 60°.

Question 10: Find the missing side length if an equilateral triangle has an altitude of 6 cm.

Answer: Side length approximately 12 cm

Question 11: A real-world scenario: A gardener designs a circular flower bed in the shape of an equilateral triangle with sides of 4 meters each. Calculate the total length of fencing needed.

Answer: 12 meters