Geometric Compositions

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?

• ∠ABD = ½∠CBD

• ∠ABD = ∠CBD

• ∠ABD = ∠ABC

• ∠CBD = ½∠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

Marsha is using a straightedge and compass to do the construction shown. Which best describes the construction Marsha is doing?

• a line through P parallel to line l
• a line through P intersecting line l
• a line through P congruent to line l
• a line through P perpendicular to line l

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

• AB ⊥ CD

• AB ≅ CD

• AE ≅ ED

• CE ≅ DE

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

Amber construced BD as shown. Which of the following statements must be true?

• BD = 2BA

• ∠CBD = 2∠ABC

• BA = BC

• ∠ABD = ∠CBD

Which of the following constructions is illustrated?

• The bisector of a given angle.

• An angle congruent to a given angle.

• The perpendicular bisector of a given segment.

• The bisector of a given segment.

The drawing shows the arcs used to construct what?

• a bisector of a given line

• a bisector of a given angle

• a segment perpendicular to the line through a given point

• an angle congruent to a given angle