Question 1: A triangle has sides of lengths 5 cm, 7 cm, and 9 cm. Is this triangle scalene? Explain why or why not.

Answer: Yes, all sides are different, so the triangle is scalene.

Question 2: Calculate the perimeter of a scalene triangle with side lengths 8 cm, 10 cm, and 12 cm.

Answer: 30

Question 3: If a scalene triangle has sides of 6 cm and 10 cm, what is the possible range for the third side length? Show your reasoning.

Answer: 4 cm < third side < 16 cm

Question 4: Construct a scalene triangle with sides of 7 cm, 9 cm, and 11 cm. Use the grid for your drawing.

Answer: Student draws a scalene triangle with the specified sides.

Question 5: Calculate the measure of the third angle in a scalene triangle where two angles are 50° and 60°. Show your working.

Answer: 70

Question 6: A real-world scenario: A triangular plot of land has sides of 15 m, 20 m, and 25 m. Is the plot potentially scalene? Justify your answer.

Answer: Yes, all sides are different, so the plot is scalene.

Question 7: In a scalene triangle, if two sides are 8 cm and 15 cm, what is the maximum possible length of the third side?

Answer: 22 cm

Question 8: Identify and correct the mistake in this reasoning: "Since all sides in a scalene triangle are different, the angles must all be different. Therefore, if two sides are equal, the triangle is not scalene."

Answer: The mistake is assuming equal sides make it not scalene; actually, equal sides mean it is not scalene, but the reasoning is incorrect as it contradicts the definition.

Question 9: A triangle with sides 9 cm, x cm, and 12 cm is scalene. Find the range for x.

Answer: 3 cm < x < 21 cm

Question 10: Challenge: Prove that in a scalene triangle, the sum of any two sides is greater than the third. Use an example with sides 7 cm, 9 cm, and 11 cm.

Answer: 7+9=16>11, 7+11=18>9, 9+11=20>7. All sums are greater than the remaining side, confirming the triangle inequality.

Question 11: Identify a common mistake when students assume all triangles with different side lengths are scalene and explain why it's incorrect.

Answer: The mistake is assuming different sides always form a scalene triangle, but some configurations can be invalid or isosceles if two sides are equal.