Question 1: Calculate the measure of each interior angle in an equilateral triangle.

Answer: 60

Question 2: If one angle of an equilateral triangle is 60°, what is the sum of the other two angles?

Answer: 120

Question 3: Construct an equilateral triangle with side length 5 cm on the grid. Ensure all sides are equal.

Answer: All sides 5cm

Question 4: True or False: An equilateral triangle always has angles measuring 45°, 45°, and 90°.

Answer: False

Question 1: A triangle has two angles measuring 60° each. Is it necessarily equilateral? Explain your reasoning.

Answer: No, because the third angle could be different; the triangle is only equilateral if all sides are equal, which is not guaranteed by two angles alone.

Question 2: A triangle has sides measuring 4 cm, 4 cm, and 6 cm. Can it be equilateral? Justify your answer.

Answer: No, because not all sides are equal; therefore, it cannot be equilateral.

Question 3: Explain why all angles in an equilateral triangle measure 60°, using the properties of triangles.

Answer: Since all sides are equal, the triangle is equilateral, and each interior angle is 60° because the sum of interior angles in a triangle is 180°, divided equally among three equal angles.

Question 1: A fencing company needs to build a triangular enclosure with sides of 6 meters each in a park. How many degrees are each of the angles inside the enclosure? Explain your reasoning.

Answer: Each angle measures 60° because the triangle is equilateral.

Question 1: Prove that an equilateral triangle is also equiangular, using geometrical reasoning.

Answer: In an equilateral triangle, all sides are equal. By the Isosceles Triangle Theorem, angles opposite equal sides are equal. Since all sides are equal, all angles are equal. The sum of interior angles is 180°, so each angle is 60°, proving the triangle is equiangular.

Question 2: If the side length of an equilateral triangle is doubled, how does the area change? Provide calculations to support your answer.

Answer: Original area = (√3/4) * (side)^2. When side doubles, new area = (√3/4) * (2 * side)^2 = (√3/4) * 4 * side^2 = 4 * original area. So, the area quadruples.

Question 1: Statement: 'All triangles with a 60° angle are equilateral.' Is this true? Explain your answer and correct any misconceptions.

Answer: No, triangles can have a 60° angle without being equilateral, such as in a right-angled triangle with one 60° angle and two unequal sides. Equilateral triangles require all sides and angles to be equal, not just one angle.

Question 2: A student says: 'In an equilateral triangle, the sides are 4 cm, 4 cm, and 6 cm.' Identify the mistake.

Answer: The sides are not all equal; therefore, the triangle cannot be equilateral. The sides must be 4 cm, 4 cm, and 4 cm.