Question 1: What is the defining characteristic of a scalene triangle?

Answer: All sides are of different lengths

Question 2: Calculate the length of side AC in a triangle with sides AB=7cm, BC=9cm, and AC=? if the triangle is scalene and the sum of sides AB and AC is 15cm.

Answer: 8

Question 3: Construct a scalene triangle with side lengths 5 cm, 7 cm, and 9 cm. Show all steps.

Answer: Student draws a triangle with sides 5, 7, 9, ensuring no two sides are equal.

Question 4: In a scalene triangle, if two sides measure 6 cm and 10 cm, what is the possible range for the third side?

Answer: 4 to 15 cm

Question 5: Calculate the angles of a scalene triangle with sides 8 cm, 15 cm, and 17 cm. Use the Law of Cosines.

Answer: Angles approximately 30°, 60°, and 90°

Question 6: A triangle has sides of lengths 10 cm, 12 cm, and 14 cm. Is it scalene? Justify your answer.

Answer: Yes, all sides are different lengths.

Question 7: If a scalene triangle has one side measuring 9 cm and another 14 cm, what is the shortest possible length of the third side?

Answer: 6

Question 8: Determine whether the triangle with sides 4 cm, 5 cm, and 9 cm is scalene. Explain.

Answer: No, because 4 + 5 = 9, which means it is degenerate, not a proper triangle.

Question 9: Plot the graph of y = 2x for x values from -5 to 5. Use the grid to sketch.

Answer: Student draws a line passing through points (-5, -10), (0, 0), and (5, 10).

Question 10: A scalene triangle has sides measuring 13 cm, 14 cm, and 15 cm. Calculate the perimeter and verify if it satisfies the triangle inequality.

Answer: Perimeter = 42 cm; sum of any two sides exceeds the third, so valid.

Question 11: Identify and correct the mistake in the following statement: 'A scalene triangle can have two equal angles.'

Answer: A scalene triangle cannot have two equal angles; all angles are different.

Question 12: Challenge: Given the side lengths 8 cm, 11 cm, and 13 cm, find the area of the scalene triangle using Heron's formula.

Answer: Approximate area = 41.2 cm²