Understanding angles (age 12+)

Question 1

When a student correctly constructs the perpendicular bisector of a line segment AB using a compass and straightedge, which statement must be true about the line they have drawn?

Accepted Answer

It passes through the midpoint of the segment and is perpendicular to it.

Answer

It forms a 45-degree angle with the segment.

Answer

It has the same length as the segment.

Answer

It runs parallel to the segment.

Question 2

Angle XYZ measures 80°. After constructing the angle bisector of angle XYZ, what is the measure of each of the two smaller angles formed?

Accepted Answer

40°

Answer

30°

Answer

50°

Answer

20°

Question 3

Which of the following describes the correct first steps for constructing the perpendicular bisector of a line segment AB using only a ruler and compass?

Accepted Answer

Place the compass point on A and draw an arc above and below the segment, then repeat the same radius from B, creating two intersecting arcs; draw the line through the intersection points.

Answer

Use the ruler to draw a straight line through A that looks perpendicular to AB.

Answer

Place the compass point on B and draw a full circle that crosses the segment AB, then draw a line through the center of the circle.

Answer

Find the midpoint of AB with a ruler, then draw a line through that point that is perpendicular to AB.

Try three questions

When a student correctly constructs the perpendicular bisector of a line segment AB using a compass and straightedge, which statement must be true about the line they have drawn?

Angle XYZ measures 80°. After constructing the angle bisector of angle XYZ, what is the measure of each of the two smaller angles formed?

Which of the following describes the correct first steps for constructing the perpendicular bisector of a line segment AB using only a ruler and compass?

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