Question 1: Construct an isosceles triangle with the two equal sides measuring 6 cm each and the base measuring 8 cm.

Answer: See full answer key

Question 2: In an isosceles triangle, the equal sides each measure 10 cm. The vertex angle is 40°. Calculate the base angles of the triangle.

Answer: 70

Question 3: If an isosceles triangle has two sides measuring 5 cm and 7 cm, which of these could be the lengths of the equal sides? Justify your answer.

Answer: 5 cm or 7 cm (since the two equal sides must be either both 5 cm or both 7 cm, and the third side can vary accordingly)

Question 4: Plot an isosceles triangle on the grid with equal sides of 4 units and a base of 6 units.

Answer: See full answer key

Question 5: An isosceles triangle has sides of 8 cm, 8 cm, and a base of 10 cm. Calculate the height of the triangle from the apex to the base.

Answer: 6

Question 6: In a real-world scenario, a bridge supports an isosceles triangle structure where the equal sides are 12 meters each. If the base is 8 meters, find the angle between the equal sides at the top.

Answer: Approx. 53°

Question 7: Determine whether the following statement is true or false: 'In an isosceles triangle, the angles opposite the equal sides are equal.' Explain your reasoning.

Answer: True

Question 8: Given an isosceles triangle with sides 9 cm, 9 cm, and 5 cm, find the measure of the vertex angle.

Answer: 126

Question 9: A triangle with sides 7 cm, 7 cm, and 10 cm is drawn. Is it isosceles? Justify your answer.

Answer: Yes, the two sides measuring 7 cm are equal, so the triangle is isosceles.

Question 10: Error Analysis: A student claims that the base angles of an isosceles triangle with equal sides of 6 cm are both 45°. Identify the mistake and correct it.

Answer: The mistake is assuming the angles are 45° without calculation. The base angles are actually 57° each, since sum of angles in triangle is 180° and vertex angle is 66°.