Lesson 9

Speedy Delivery

• Let’s use perpendicular bisectors.

Problem 1

Which construction can be used to determine whether point $$C$$ is closer to point $$A$$ or point $$B$$?

A:

Construct triangle $$ABC$$.

B:

Construct a line perpendicular to segment $$AB$$ through point $$C$$.

C:

Construct the bisector of angle $$ACB$$.

D:

Construct the perpendicular bisector of segment $$AB$$.

Problem 2

The diagram is a straightedge and compass construction. Lines $$\ell$$, $$m$$, and $$n$$ are the perpendicular bisectors of the sides of triangle $$ABC$$. Select all the true statements.

A:

Point $$E$$ is closer to point $$A$$ than it is to point $$C$$.

B:

Point $$L$$ is closer to point $$B$$ than it is to point $$A$$.

C:

Point $$D$$ is closer to point $$B$$ than it is to point $$C$$.

D:

Point $$J$$ is closer to point $$A$$ than it is to point $$B$$ or point $$C$$.

E:

Point $$K$$ is closer to point $$C$$ than it is to point $$A$$ or point $$B$$.

F:

Point $$L$$ is closer to point $$C$$ than it is to point $$A$$ or point $$B$$.

Problem 3

Decompose the figure into regions that are closest to each vertex. Explain or show your reasoning.

Problem 4

Which construction could be used to construct an isosceles triangle $$ABC$$ given line segment $$AB$$?

A:

Mark a third point $$C$$ not on segment $$AB$$. Draw segments $$AC$$ and $$BC$$.

B:

Label a point $$C$$ on segment $$AB$$ and construct a line perpendicular to $$AB$$ through point $$C$$. Draw segments $$AC$$ and $$BC$$.

C:

Construct the perpendicular bisector of segment $$AB$$. Mark the intersection of this line and $$AB$$ and label it $$C$$. Draw segments $$AC$$ and $$BC$$.

D:

Construct the perpendicular bisector of segment $$AB$$. Mark any point $$C$$ on the perpendicular bisector except where it intersects $$AB$$. Draw segments $$AC$$ and $$BC$$.

Problem 5

Select all true statements about regular polygons.

A:

All angles are right angles.

B:

All angles are congruent.

C:

All side lengths are equal.

D:

There are exactly 4 sides.

E:

There are at least 3 sides.

(From Unit 1, Lesson 7.)

Problem 6

This diagram shows the beginning of a straightedge and compass construction of a rectangle.

The construction followed these steps:

1. Start with two marked points $$A$$ and $$B$$
2. Use a straightedge to construct line $$AB$$
3. Use a previous construction to construct a line perpendicular to $$AB$$ passing through $$A$$
4. Use a previous construction to construct a line perpendicular to $$AB$$ passing through $$B$$
5. Mark a point $$C$$ on the line perpendicular to $$AB$$ passing through $$A$$

Explain the steps needed to complete this construction.

(From Unit 1, Lesson 7.)

Problem 7

This diagram is a straightedge and compass construction. Is it important that the circle with center $$B$$ passes through $$D$$ and that the circle with center $$D$$ passes through $$B$$? Show or explain your reasoning.

(From Unit 1, Lesson 5.)