# Polygon Similarity

## Introduction

Observe the figures: Figure A Figure B Figure C

They represent rectangles with different scales. Note that the three rectangles have the same shape but different sizes. We say they are similar figures.

In these figures we can identify:
AB - distance between THE and B (length of rectangle).
CD - distance between Ç and D (width of rectangle). - sharp angles formed by the segments .

Measuring line segments and and the angles ( ) of the figures, we can organize the following table:

 m ( ) m ( ) angle Fig. C 3.9 cm 1.3 cm = 90º Fig. B 4.5 cm 1.5 cm = 90º Fig. A 6.0 cm 2.0 cm = 90º

Notice that:

• The corresponding angles in the three figures have equal measurements;
• The measurements of the corresponding segments are proportional; From this example, we can conclude that two or more figures are similar in geometry when:

• the corresponding angles have equal measurements;

• the measurements of the corresponding segments are proportional;

• The elements of the figures are common.

Other examples of Similar figures:   Same shapes and different sizes

Next: Similar Polygons