Question 1: In an isosceles triangle, the two equal angles each measure 65°. Find the measure of the third angle.

Answer: 50

Question 2: A triangle has angles of 40° and 70°, and it is isosceles. What is the measure of the third angle?

Answer: 70

Question 3: Construct an isosceles triangle with a base of 6 cm and equal sides of 8 cm.

Answer: student drawn

Question 4: In an isosceles triangle, the equal sides are each 10 cm. The base angles are each 45°. Calculate the height from the apex to the base.

Answer: 7.07

Question 5: A pair of isosceles triangles are joined at their bases to form a kite. If each of the equal angles in the triangles measures 70°, what is the measure of the angles where the triangles meet?

Answer: 40

Question 6: A student mistakenly claims that all isosceles triangles have two right angles. Explain why this is incorrect.

Answer: because in isosceles triangles, only the angles opposite the equal sides are equal; right angles are not mandatory.

Question 7: A triangle has two equal sides of 5 cm each, and the vertex angle measures 60°. Find the length of the base if the triangle is isosceles and the height from the vertex bisects the base.

Answer: 4.33

Question 8: Determine whether the following triangle is isosceles: angles are 70°, 70°, and 40°.

Answer: Yes

Question 9: Plot the graph of y=2x for x-values from -3 to 3. Use the grid to draw the line.

Answer: student drawn

Question 10: Construct an isosceles triangle with a vertex angle of 100° and equal sides of 7 cm. Label all angles.

Answer: student drawn

Question 11: In an isosceles triangle, the base angles are each 55°. Find the measure of the vertex angle.

Answer: 70

Question 12: Identify and correct the mistake in the following statement: 'An isosceles triangle always has one right angle.'

Answer: because an isosceles triangle does not necessarily have a right angle; it can have all angles acute or obtuse.