## Congruence and Construction

**Congruent Figures and Constructions**

Two figures with the same size and shape are congruent. Corresponding, or matching, angles and line segments of congruent figures are congruent. That is, the corresponding sides have the same measures and the corresponding angles have the same measures. At this grade level, students will construct congruent line segments, congruent angles, and equilateral triangles. A construction is completed with only a safe drawing compass and a straightedge. A ruler may be used to check a construction.

**Similar Figures**

Similar figures have the same shape but not necessarily the same size. The corresponding angles of similar figures are congruent. If two figures are similar, the lengths of their corresponding line segments are proportional—that is, they have the same ratio. Congruent figures are similar figures with a ratio of 1:1 between corresponding line segments.

**Transformations in the Plane**

A geometric transformation changes the position or size of a figure in the plane without changing the shape of the figure. At this grade level, the study of size transformations is limited to studying similar figures with no mention of transformations. All transformations studied in this chapter involve only translations, rotations, and reflections.

A **translation** slides a figure along a line in one direction. A **rotation** turns a figure about a given point. A **reflection** flips the figure across a line of reflection, thus producing a mirror image. At this grade level, it may be easier for students to complete transformations by working on grid paper.

**Teaching Model 15.3:** Symmetry