Question

unit 42 - lesson 43 exit ticket: line segment ef has been reflected across line r shown below to produce image segment ef. segment ef has also been drawn.
(a) what type of angle does line r make with ff?
(b) give two pairs of congruent segments.

Explanation:

Step1: Recall angle - types in reflection

When a line segment is reflected across a line, the line of reflection is the perpendicular bisector of the segment joining corresponding points. The angles formed between the line of reflection and the original and reflected line - segments are right angles. So, line \(r\) makes right angles with \(\overline{EF}\) and \(\overline{E'F'}\).

Step2: Recall congruent - segment properties in reflection

In a reflection, the original line - segment and its reflected image are congruent. So, \(\overline{EF}\cong\overline{E'F'}\). Also, if we consider the segments formed by the intersection of the line of reflection with the segments joining corresponding points (e.g., the segments from \(E\) to the foot of the perpendicular on \(r\) and from \(E'\) to the foot of the perpendicular on \(r\)), they are congruent. Let the intersection of \(r\) and \(\overline{EE'}\) be \(M\) and the intersection of \(r\) and \(\overline{FF'}\) be \(N\). Then \(\overline{EM}\cong\overline{E'M}\) and \(\overline{FN}\cong\overline{F'N}\).

Answer:

(a) Right angles
(b) \(\overline{EF}\cong\overline{E'F'}\), \(\overline{EM}\cong\overline{E'M}\) (where \(M\) is the intersection of \(r\) and \(\overline{EE'}\))