G1.5 Assignment: Geometric Constructions

When copying line segment AB using a straight edge and a compass, the compass should be used to:

• Draw an arc above point A

• Measure the length of segment AB

• Draw an arc between point A and point B

• Measure half the length of line segment AB

Suppose we wish to construct a perpendicular bisector of line segment EF. We can correctly begin by placing the compass point on E and marking off the distance to which point?

• A

• B

• C

• D

Suppose we wish to construct angle EFG congruent to angle DBC using a compass and straightedge. Which step would be correct to do first?

• Place the compass point at B

• Place the compass point at C

• Place the straightedge along A and C

• Place the straightedge along C and D

When bisecting an angle, the straightedge should be used to:

• Mark the point M

• Measure the angle AOB

• Copy the angle with an arc

• Connect point M and vertex O

Which diagram shows a correct mathematical construction using only a compass and a straightedge to bisect an angle?

• A

• B

• C

• D

What geometric construction is shown in the diagram below?

• an angle bisector

• a line parallel to a given line

• an angle congruent to a given angle

• a perpendicular bisector of a segment

Given: angle A. What is the first step in constructing the angle bisector of angle A?

• Draw ray AD

• Draw a line segment connecting points B and C.

• From points B and C, draw equal arcs that intersect at D.

• From point A, draw an arc that intersects the sides of the angle at points B and C.

Based on the construction, which statement must be true?

• m∠ABD = ½m∠CAD

• m∠ABD = m∠CBD

• m∠ABD = m∠ABC

• m∠CBD = ½m∠ABD

Line segment AB is shown in the diagram. Which two sets of construction marks, labeled I, II, III, and IV, are part of the construction of the perpendicular bisector of line segment AB?

• I and II

• I and III

• II and III

• II and IV

Based on the construction, which conclusion is not always true?

• A

• B

• C

• D