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: Construct an equilateral triangle with side length 6cm. What are the measures of all its angles?

Answer: 60

Question 4: A regular hexagon is divided into equilateral triangles. How many equilateral triangles are formed?

Answer: 6

Question 5: In an equilateral triangle, if one angle is increased by 5°, what is the measure of the new angle?

Answer: 65

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

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, and the sum of angles is 180°, so each must be 60°.

Question 7: A triangle has two sides of length 5cm and 5cm. To be equilateral, what should the third side be? Show your reasoning.

Answer: 5cm

Question 8: If an equilateral triangle is scaled up so that each side becomes 10cm, what is the perimeter?

Answer: 30cm

Question 9: Challenge: Prove that in an equilateral triangle, the medians are also the altitudes and angle bisectors.

Answer: In an equilateral triangle, all sides are equal, and the medians, altitudes, and angle bisectors coincide because of symmetry and equal side lengths, dividing the triangle into congruent parts. This can be shown through coordinate geometry or congruence theorems.

Question 10: Identify and correct the mistake: In an equilateral triangle, two angles are 60° and 70°.

Answer: The mistake is that the angles in an equilateral triangle are always 60°. Having 70° violates the property. The corrected angles are both 60°.

Question 11: Real-world scenario: A triangular signpost has an equilateral triangular section. If each side of the section measures 3 meters, what is the total length of the perimeter?

Answer: 9 meters