Question 1: Construct a triangle with sides 5 cm, 7 cm, and 9 cm. Use the grid to accurately draw the triangle.

Answer:

Question 2: Given sides of 4 cm, 6 cm, and 8 cm, verify if such a triangle can exist. Show your reasoning.

Answer: Yes, since the sum of any two sides is greater than the third (4+6>8, 4+8>6, 6+8>4).

Question 3: Construct a triangle with sides of 3 cm, 5 cm, and 8 cm. Is this possible? Explain.

Answer: No, because 3 + 5 = 8, which is not greater than 8, so a triangle cannot be formed.

Question 4: Construct a triangle with sides 6 cm, 6 cm, and 10 cm. Use the grid to draw it accurately.

Answer:

Question 5: Calculate the perimeter of a triangle with sides 7 cm, 9 cm, and 12 cm.

Answer: 28 cm

Question 6: Construct and label a triangle with sides 8 cm, 10 cm, and 12 cm. Show all steps.

Answer:

Question 7: Determine whether the triangle with sides 2 cm, 4 cm, and 7 cm exists. Justify your answer.

Answer: No, because 2 + 4 = 6, which is less than 7, so the triangle cannot exist.

Question 8: Construct a triangle with sides 10 cm, 12 cm, and 15 cm. Use the grid for accuracy.

Answer:

Question 9: Construct a triangle with sides 3 cm, 4 cm, and 6 cm. Calculate its area if possible (use Heron’s formula).

Answer: Heron's semi-perimeter s = (3+4+6)/2=6.5; Area = √[6.5(6.5-3)(6.5-4)(6.5-6)] ≈ 5.9 cm²

Question 10: Identify the common mistake students make when constructing a triangle with sides 8 cm, 15 cm, and 25 cm, and explain how to avoid it.

Answer: A common mistake is assuming the sides form a triangle without verifying the triangle inequality. To avoid this, always check that the sum of any two sides exceeds the third.