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## Basic geometry and measurement

### Course: Basic geometry and measurement>Unit 14

Lesson 7: Congruence and similarity

# Similarity & transformations

## Problem

Erin was able to map line segment start overline, A, B, end overline onto line segment start overline, C, B, end overline using a rotation and a dilation.
Quadrilateral O N M L and quadrilateral O P Q R in the first quadrant of a coordinate plane. In quadrilateral O N M L, point O is at seven, five, point N is at five, nine, point M is at one, three, and point L is at three, one. In quadrilateral O P Q R, point O is at seven. five, point P is at eight, seven, point Q is at ten, four, and point R is at nine, three. There is a dashed outline for quadrilateral O P Q R to show its image after a reflection over a vertical line that goes through point O. There are rays from the dashed outline for quadrilateral O P Q R to highlight that a dilation makes the new quadrilateral O P Q R coincide with quadrilateral O N M L.
Erin concluded:
"I was able to map line segment start overline, A, B, end overline onto line segment start overline, C, B, end overline using a sequence of rigid transformations and dilations, so the figures are similar."
What error did Erin make in her conclusion?