Question

1. in the diagram below, \\( \angle p ^ { prime } q ^ { prime } r ^ { prime } \\) is the image of \\( \angle p q r \\) after a reflection across line \\( m \\).

(a) using a straightedge, draw a segment from each point to its image
point. in other words, draw \\( \overline { p p ^ { prime } } \\), \\( \overline { q q ^ { prime } } \\), and \\( \overline { r r ^ { prime } } \\).
(b) use one term to describe the relationship between line \\( m \\) and the
segments you drew in (a).
(c) if \\( m \angle p q r = 34 ^ { \circ } \\), then what is the measure of \\( \angle p ^ { prime } q ^ { prime } r ^ { prime } \\)? explain.

1. in the diagram shown, right triangle \\( e f g \\) has side \\( \overline { f g } \\) on line \\( r \\). if \\( \triangle e f g \\) was

reflected across line \\( r \\):
(a) why would points \\( f \\) and \\( g \\) not move under this reflection?
(b) use a compass and straightedge to locate point \\( e ^ { prime } \\) and draw \\( \triangle e ^ { prime } f ^ { prime } g ^ { prime } \\).
n-gen math \\( ^ { circ } \\) geometry - unit 2 - rigid motions and congruence - lesson 5 (v11.11.24)
emathinstruction, red hook, ny 12571, \\& 2023

Explanation:

2.(b)

Reflection across a line implies that the line is the perpendicular bisector of the segments joining pre - image and image points.

A reflection is a rigid motion. Rigid motions (isometries) preserve the measure of angles. Since \(\angle P'Q'R'\) is the image of \(\angle PQR\) under a reflection (a rigid motion), the measure of \(\angle P'Q'R'\) is equal to the measure of \(\angle PQR\).

A reflection across a line leaves points on the line of reflection unchanged. Points \(F\) and \(G\) lie on the line \(r\) (the line of reflection).

Answer:

Perpendicular bisector

2.(c)