Question 1: Construct a triangle with sides of length 5 cm, 7 cm, and 8 cm. Label the vertices.

Answer: Constructed triangle with specified sides

Question 2: Using the given sides of 6 cm, 9 cm, and 10 cm, verify if such a triangle is possible. Explain your reasoning.

Answer: Yes, because the sum of any two sides is greater than the third.

Question 3: Construct a triangle with sides 4 cm, 6 cm, and 9 cm. Is this possible? Justify your answer.

Answer: No, because 4 + 6 = 10, which is not greater than 9.

Question 4: Construct a triangle with sides 3.5 cm, 4.2 cm, and 5.0 cm. Show all steps.

Answer: Constructed triangle with specified sides

Question 1: Given three sides of lengths 8 cm, 10 cm, and 12 cm, construct the triangle. Then, determine if the triangle is acute, right-angled, or obtuse. Show your working.

Answer: Constructed triangle; check angles using cosine rule or Pythagoras; likely obtuse

Question 2: A triangle has sides of 7 cm, 9 cm, and 11 cm. If the longest side is increased by 2 cm, will the sides still form a triangle? Explain.

Answer: Yes, since 7 + 9 = 16 > 13 (new longest side), so triangle is possible.

Question 3: Construct a triangle with sides 6 cm, 8 cm, and 10 cm. Verify if it is a right triangle.

Answer: Yes, because 6^2 + 8^2 = 36 + 64 = 100, which equals 10^2.

Question 4: Explain why sides 5 cm, 7 cm, and 13 cm cannot form a triangle.

Answer: Because 5 + 7 = 12, which is less than 13, so the triangle inequality is violated.

Question 1: A surveyor needs to construct a triangular plot with sides measuring 12 m, 15 m, and 20 m. Describe the steps they would take to construct this triangle accurately.

Answer: Use a ruler and compass to draw the first side, then construct the other sides, ensuring each length is accurate, and verify with a ruler.

Question 2: A builder needs to frame a triangular support with sides of 3 m, 4 m, and 5 m. Explain why it is important to verify side lengths before construction.

Answer: To ensure the triangle can be constructed properly and is stable; verify triangle inequality first.

Question 1: Construct a triangle with sides of lengths 9 cm, 12 cm, and 15 cm. Confirm whether it is a right triangle and explain your reasoning.

Answer: Yes, because 9^2 + 12^2 = 81 + 144 = 225, which equals 15^2; so it is a right triangle.

Question 2: Given sides 7 cm, 24 cm, and 25 cm, determine if the triangle is scalene, isosceles, or equilateral. Justify your answer.

Answer: Scalene, since all sides are different lengths.

Question 1: Construct a triangle with sides of 6.5 cm, 7.2 cm, and 8.1 cm. Show all steps.

Answer: Constructed triangle with specified sides

Question 2: Construct a triangle with sides 5 cm, 6 cm, and 11 cm. Is this possible? Explain and justify.

Answer: No, because 5 + 6 = 11, which is not greater than 11, so construction is impossible.

Question 1: A student claims they can construct a triangle with sides 3 cm, 4 cm, and 8 cm. Explain what mistake they made and why this is not possible.

Answer: They failed to check the triangle inequality; since 3 + 4 = 7, which is less than 8, no triangle can be formed.

Question 2: A student draws two sides of lengths 5 cm and 7 cm, then tries to construct the third side as 10 cm. Explain why this does not form a triangle.

Answer: Because 5 + 7 = 12, which is less than 10, so the triangle inequality is violated.