Similar Figures Done by: Gana El Masry

Similar Figures Figures that are the same shape but not necessarily the same size are called similar figures. The triangles shown on the next slide are similar.

Similar Figures (continued) Similar figures also have the following properties: Corresponding sides are proportional. The ratios of the corresponding sides are equal. Corresponding angles are equal.

Example For example, consider the following squares. Thus the squares are similar figures as their corresponding sides are proportional and their corresponding angles are equal.

Important note Each side of figure PQRS has been multiplied by 2 to obtain the sides of ABCD. The number 2 is called the scale factor. Similar figures are equiangular, that means the corresponding angles of similar figures are equal. Corresponding angles are angles in the same relative position in polygons with an equal number of sides. Corresponding sides are matching sides of two or more polygons.

Important note Corresponding angles of two or more similar polygons are in the same relative position. Corresponding sides of two or more similar polygons are in the same relative position. When naming similar figures, list the corresponding angles in the same order. Ratios are required to determine if two figures are similar. This lesson could be called similar figures or similar figures and proportions.

Quick Revision A ratio is a comparison of two quantities by division. A rate is a ratio that compares two quantities measured in different units. The unit rate is a rate whose denominator is 1 when it is written as a fraction.

Quick Revision

Quick Revision (Continued)

Some picture examples.

Some picture Examples

More information (congruent figures) In real life, we use the word "similar" to mean different things. The term is somewhat vague. In math, it has a special definition. See the picture below. In math, two figures are called similar if they are the same shape, but different sizes, such as the turtles in the lower half of the picture. It doesn't matter if they are rotated or not. Two figures are congruent if they are exactly the same size and the same shape, such as the turtles in the top half of the picture in the next slide. Again, rotation doesn't matter at all.

Questions Is the following figures similar or congruent? It is Congruent, the rotation of the figure doesn’t matter at all

Questions If you want only to rotate, translate or reflect then the figure is …………………. If you need to resize the figure is ………………….. What does this sign mean? (~) ……………………are matching sides of two or more polygons. ………………………are angles in the same relative position in polygons with an equal number of sides.

Thank You Done by: Gana Mohamed El Masry Grade: 7 To our sweet/great teacher: Miss Sahar.

Miss Sahar Metwalli