# Lesson 6

Construction Techniques 4: Parallel and Perpendicular Lines

### Problem 1

Which of the following constructions would help to construct a line passing through point $$C$$ that is perpendicular to the line $$AB$$?

A:

Construction of an equilateral triangle with one side $$AB$$

B:

Construction of a hexagon with one side $$BC$$

C:

Construction of a perpendicular bisector through $$C$$

D:

Construction of a square with one side $$AB$$

### Problem 2

Two distinct lines, $$\ell$$ and $$m$$, are each perpendicular to the same line $$n$$. Select all the true statements.

A:

Lines $$\ell$$ and $$m$$ are perpendicular.

B:

Lines $$\ell$$ and $$n$$ are perpendicular.

C:

Lines $$m$$ and $$n$$ are perpendicular.

D:

Lines $$\ell$$ and $$m$$ are parallel.

E:

Lines $$\ell$$ and $$n$$ are parallel.

F:

Lines $$m$$ and $$n$$ are parallel.

### Problem 3

This diagram is a straightedge and compass construction of the bisector of angle $$BAC$$. Only angle $$BAC$$ is given. Explain the steps of the construction in order. Include a step for each new circle, line, and point.

### Solution

(From Unit 1, Lesson 5.)

### Problem 4

This diagram is a straightedge and compass construction of a line perpendicular to line $$AB$$ passing through point $$C$$. Which segment has the same length as segment $$EA$$?

A:

$$EC$$

B:

$$ED$$

C:

$$BE$$

D:

$$BD$$

### Solution

(From Unit 1, Lesson 5.)

### Problem 5

This diagram is a straightedge and compass construction. Which triangle is equilateral? Explain how you know.

### Solution

(From Unit 1, Lesson 4.)

### Problem 6

In the construction, $$A$$ is the center of one circle, and $$B$$ is the center of the other. Name the segments in the diagram that have the same length as segment $$AB$$.

### Solution

(From Unit 1, Lesson 2.)

### Problem 7

This diagram is a straightedge and compass construction. $$A$$ is the center of one circle, and $$B$$ is the center of the other.

1. Name a pair of perpendicular line segments.
2. Name a pair of line segments with the same length.

### Solution

(From Unit 1, Lesson 3.)

### Problem 8

$$A$$, $$B$$, and $$C$$ are the centers of the 3 circles. Select all the segments that are congruent to $$AB$$.

A:

$$HF$$

B:

$$HA$$

C:

$$CE$$

D:

$$CD$$

E:

$$BD$$

F:

$$BF$$