Geometry Geometric Constructions Test with Point Values (PDF)

1. Why must the compass radius be more than half of AB? (1 point)
2. AB = 20 and AP = 13. Find PM. (1 point)
3. P is on the bisector with PA = 3x + 5 and PB = 5x – 9. Find x. (1 point)

Ray VR bisects angle PVQ. \(m\angle PVR = (5x + 6)^{\circ}\) and \(m\angle RVQ = (7x – 14)^{\circ}\). Find x and \(m\angle PVQ\).

Explain why triangle ABC, constructed by drawing arcs of radius AB from A and from B, is equilateral. If AB = 9, find the height of the triangle.

A regular hexagon is inscribed in a circle of radius 10. Find its perimeter and the length of the longest diagonal.

A square is inscribed in a circle of radius 7. Find the side length and the area of the square.

List in order the steps to bisect an angle: (a) draw the ray from the vertex through the crossing point, (b) from each of the two points on the rays, draw arcs of equal radius that cross, (c) draw an arc centered at the vertex that crosses both rays.

Describe how to construct a line through a point P that is parallel to a given line l, and name the angle relationship that makes your lines parallel.

Find an equation of the perpendicular bisector of the segment with endpoints (-2, 3) and (4, 7).

A fountain is to be placed at a point equally far from two park entrances A and B, which are 60 yards apart. The fountain must also be 50 yards from A. Describe where the fountain lies, find its distance from B, and find its distance from the midpoint of AB.