Question 1: An isosceles triangle has two equal sides of length 7 cm. The base is 10 cm. Calculate the measure of each of the equal angles.

Answer: 64°

Question 2: Construct an isosceles triangle with two equal sides of 6 cm and a base of 8 cm. Label the angles.

Answer: Construction on grid with angles marked approximately 53° at the equal sides

Question 3: In an isosceles triangle, the vertex angle measures 40°. What are the measures of the other two equal angles?

Answer: 70°

Question 4: A triangle has angles measuring 50° and 60°. If the triangle is isosceles, what are the possible measures of the third angle?

Answer: 70° or 50°

Question 5: Calculate the length of the third side in an isosceles triangle where the equal sides are 8 cm and the base is 12 cm.

Answer: Approx. 5.2 cm

Question 6: An isosceles triangle has sides of 5 cm, 5 cm, and 8 cm. Is this triangle valid? Explain your reasoning.

Answer: Yes, because the sum of the two equal sides exceeds the third side (5+5=10 > 8).

Question 7: Plot the graph of y = 2x for x-values between -5 and 5.

Answer: Line passing through points (-5,-10), (0,0), (5,10)

Question 8: Construct an isosceles triangle with a vertex angle of 30° and equal sides of 10 cm. Label the base and the angles.

Answer: Constructed with base approximately 17.3 cm, angles at base approximately 75°

Question 9: In an isosceles triangle, if the two equal sides measure 9 cm each, what is the height drawn from the vertex opposite the base?

Answer: Approx. 7.8 cm

Question 10: Identify and correct the mistake: 'In an isosceles triangle, the base angles are always equal.'

Answer: Correct statement; mistake is not present