In details

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. C3.9 cm1.3 cm= 90º
Fig. B4.5 cm1.5 cm= 90º
Fig. A6.0 cm2.0 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