Geometric Constructions Test – Geometry Math (Printable PDF)

Question 1 Order the bisector steps (2 points)

Put these steps for bisecting ∠XOY in order by writing the numbers.

1. Draw ray OZ from the vertex through the crossing point Z.
2. With the compass point on O, draw an arc that crosses both sides at X and Y.
3. With the same opening, draw arcs from X and from Y that cross at Z.
4. Keep the compass setting equal on both of the last two arcs and wider than half of XY.

Question 2 Perpendicular bisector (3 points)

Segment AB is 15.4 centimeters long. Its perpendicular bisector is constructed with arcs meeting at P and Q and crossing AB at M.

1. Find AM. (1 point)
2. What must the compass opening exceed? (1 point)
3. Which theorem shows that P is equidistant from A and B? (1 point)

Question 3 Copy an angle (2 points)

∠ABC = 57° is copied to a new vertex D. Find the measure of the copy (1 point). Which two chords must be equal for the copy to be exact? (1 point)

Question 4 Hexagon in a circle (3 points)

A regular hexagon is inscribed in a circle of radius 7.5 centimeters by stepping the radius around the circle.

1. Find the side length. (1 point)
2. Find the perimeter. (1 point)
3. Find the central angle for one side. (1 point)

Question 5 Inscribed square (3 points)

A square is inscribed in a circle of radius 12 centimeters.

1. Find the length of the diagonal. (1 point)
2. Find the side length to the nearest tenth. (1 point)
3. Find the area. (1 point)

Question 6 Prove the triangle is equilateral (3 points)

Arcs centered at A and B, each with radius AB, meet at C. Prove that △ABC is equilateral.

Question 7 Midpoint and perpendicular slope (2 points)

Segment AB has endpoints A(2, −3) and B(8, 5). Find its midpoint (1 point) and the slope of its perpendicular bisector (1 point).

Question 8 Parallel line construction (2 points)

A line through P is built by copying a 65° corresponding angle at P. Name the theorem that proves the new line parallel to the original (1 point), and give the measure of the alternate interior angle (1 point).