Question 1: Construct a triangle where one angle measures 50°, the included side is 6 cm, and the other angle is 60°. Verify your construction. (Follow the steps carefully.)

Answer: Completed triangle with correct angles and side length

Question 2: A student constructs a triangle with angles 45° and 70°, and the included side is 5 cm. They mark the second angle as 75° by mistake. Identify the error and explain why the construction is incorrect.

Answer: The student incorrectly marked the second angle as 75°, which violates the sum of angles in a triangle. The correct third angle should be 65°.

Question 3: Plot and construct a triangle with angles 40° and 60°, and an included side of 7 cm. Then, measure the third angle and verify the construction.

Answer: Third angle measures 80°; construction verified with correct angles and side length.

Question 4: An error was made where the included side was drawn incorrectly. Describe two common mistakes students make when constructing the included side and how to avoid them.

Answer: Mistake 1: Drawing the side outside the angle; fix by ensuring the side connects the two rays at their vertex. Mistake 2: Wrong length measurement; ensure precise use of a ruler.

Question 5: Given a triangle with angles 55° and 65°, and the included side of 8 cm, construct the triangle. Then, verify if the sum of the angles matches expectations.

Answer: Third angle is 60°, total 180°, confirming correct construction.

Question 6: A student claims they can construct a triangle with angles 30° and 80° and an included side of 4 cm, but the triangle cannot be formed. Explain why and what the maximum side length could be for these angles.

Answer: Because the sum of angles is 110°, the third angle is 70°, and the side length must satisfy the Law of Sines. The maximum side length depends on the configuration, but excessively long sides are impossible with these angles.

Question 7: Construct a triangle with angles 35° and 75°, and an included side of 9 cm. Then, determine the length of the third side using the Law of Cosines.

Answer: Third side length approximately 8.4 cm.

Question 8: Identify and correct the common misconception: Some students think the side length in an ASA construction can be arbitrary. Why is this incorrect?

Answer: Because the side length is included between the two specific angles, it directly influences the shape of the triangle; it cannot be arbitrary if the angles are fixed.

Question 9: Using the given angles 60° and 80°, and the included side 10 cm, construct the triangle. Then, find the other two sides using the Law of Sines or Cosines.

Answer: Other sides approximately 8.7 cm and 12.2 cm.

Question 10: A student tries to construct a triangle with angles 50° and 60°, but the constructed triangle does not have the correct shape. What is a common mistake in such constructions, and how can it be avoided?

Answer: Common mistake: incorrect use of the protractor or ruler leading to wrong angles or side length. To avoid, verify measurements carefully after each step.

Question 11: Challenge: Given two angles 45° and 70°, and a side length of 6 cm between them, construct the triangle and determine whether multiple such triangles can be formed with the same parameters. Explain your reasoning.

Answer: Since the sum of the angles is less than 180°, multiple triangles (ambiguous case) can be formed depending on the position of the third vertex relative to the base.