# 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 \(AB\)?

Construction of an equilateral triangle with one side \(AB\)

Construction of a hexagon with one side \(BC\)

Construction of a perpendicular bisector through \(C\)

Construction of a square with one side \(AB\)

### Solution

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### Problem 2

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

Lines \(\ell\) and \(m\) are perpendicular.

Lines \(\ell\) and \(n\) are perpendicular.

Lines \(m\) and \(n\) are perpendicular.

Lines \(\ell\) and \(m\) are parallel.

Lines \(\ell\) and \(n\) are parallel.

Lines \(m\) and \(n\) are parallel.

### Solution

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### 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

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(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 \(EA\)?

\(EC\)

\(ED\)

\(BE\)

\(BD\)

### Solution

### Problem 5

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

### Solution

### 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

### 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.

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

### Solution

### Problem 8

\(A\), \(B\), and \(C\) are the centers of the 3 circles. Select **all **the segments that are congruent to \(AB\).

\(HF\)

\(HA\)

\(CE\)

\(CD\)

\(BD\)

\(BF\)