Question

3 from unit 1, lesson 6 consider this diagram. to construct a line passing through the point c that is parallel to the line ab, the first step is to create a line through c perpendicular to line ab. what is the next step? a construct an equilateral triangle with side cd. b construct a line through point b perpendicular to line ab. c construct a segment with the same length as segment ab with endpoint c. d construct a line through point c perpendicular to line cd. 4 from unit 1, lesson 6 jada wanted to construct a line perpendicular to line l through point c. the diagram shows her construction. what was her mistake?

Explanation:

Step1: Recall parallel - line construction

To construct a line parallel to line $AB$ through point $C$, after constructing a line through $C$ perpendicular to $AB$ (line $CD$), the next step is to construct a line through point $C$ perpendicular to line $CD$. This new line will be parallel to $AB$ due to the properties of perpendicular and parallel lines (if two lines are perpendicular to the same line, they are parallel).

Step2: Analyze Jada's construction

Without seeing the full - details of Jada's construction steps, a common mistake in constructing a line perpendicular to a given line $l$ through a point $C$ is that the arcs drawn from point $C$ to intersect line $l$ may not be of equal radius on both sides of the point of intersection with line $l$. This can lead to an incorrect perpendicular line construction.

Answer:

1. D. Construct a line through point $C$ perpendicular to line $CD$.
2. A common mistake could be that the arcs drawn from point $C$ to intersect line $l$ are not of equal radius on both sides of the intersection point with line $l$.