Question 1: Construct an angle of 60°. Using a compass, bisect this angle and label the bisector.

Answer: Bisector constructed, dividing the angle into two 30° angles.

Question 2: Given a triangle with vertices A, B, and C, construct the bisector of angle at A.

Answer: Bisector drawn from A to the opposite side, dividing the angle into two equal parts.

Question 3: Construct a triangle with sides of length 5 cm and 7 cm, and then bisect one of its angles.

Answer: Bisector constructed at the chosen angle, dividing it into two equal angles.

Question 4: Plot the graph of y=2x for x from 0 to 5 on the grid.

Answer: Points plotted at (0,0), (1,2), (2,4), (3,6), (4,8), (5,10).

Question 5: Construct an angle of 45°, then bisect it accurately with a compass. Label the bisector.

Answer: Bisector drawn dividing the 45° angle into two 22.5° angles.

Question 6: Construct a triangle with sides 6 cm, 8 cm, and 10 cm. Bisect the largest angle.

Answer: Bisector drawn at the largest angle, dividing it into two equal parts.

Question 7: Construct an inscribed circle in a triangle, using compass and straightedge, and indicate the incenter.

Answer: Incenter located at the intersection of the angle bisectors, circle inscribed touching all sides.

Question 8: Identify and correct this common mistake: attempting to bisect an angle by drawing arcs of different radii from the vertex.

Answer: Mistake: Using different radii causes the arcs to not intersect correctly; correction: use the same radius for both arcs.

Question 9: Given two intersecting lines, construct their angle bisectors and mark the incenter of the triangle formed.

Answer: Bisectors drawn from each vertex, meeting at the incenter, which is equidistant from all sides.

Question 10: Construct a 70° angle and bisect it. Then, measure the two resulting angles to verify they are equal.

Answer: Two 35° angles confirmed through measuring with a protractor after construction.

Question 11: Challenge: Construct an angle of 90°, bisect it, then extend the bisector to meet a line parallel to one side of the angle. Describe the steps.

Answer: Construct 90° angle, bisect into two 45° angles, draw parallel line, and extend bisector to meet it, verifying equal angles.