Similar Polygons

What is a polygon? A plane figure that has three or more sides and each side intersects exactly two other sides. Examples: square, triangle, trapezoid…

What are similar polygons? Similarity - Two polygons that have corresponding angles that are congruent and the lengths of corresponding sides are proportional. The symbol for “is similar to” is It is like the congruent symbol without the equal sign.

Angles and Sides in Similar Polygons ∠A ≅ ∠ E ∠B ≅ ∠ F ∠C ≅ ∠ G Sides AB ~ EF AC ~ EG BC ~ FG A ΔABC ~ ΔEFG E B C F G

What does that mean? Corresponding angles are congruent Lengths of corresponding sides are proportional Thus, ABCD ~ EFGH

The proportions of the lengths of the corresponding sides of similar polygons are always equal. The ratio of the lengths of two corresponding sides is called the scale factor. The scale factor for the previous example is 2:1 or just 2.

How can we know the length of sides in similar figures? If two figures are similar, one figure is an enlargement of the other. The scale factor tells the amount of enlargement or reduction. Example 1: If a copy machine is used to copy a drawing or picture, the copy will be similar to the original. Original Copy Exact Copy Copy machine set to 100% Scale Factor is 1:1 Original Copy Enlargement Copy machine is set to 200% Scale Factor is 1:2 Original Copy Reduction Copy machine is set to 50% Scale Factor is 2:1

Example 2: Quadrilaterals ABCD and FGCE are similar. *Hint - draw them separately. (1) What is corresponding side of AD ? (2) What is scale factor? (3) What is corresponding side of GC? (4) How long is side GC? (5) How long is side BC? (6) How long is side DC? FE 3:1 BC 5 5+10=15 DC=12

Example 1: The triangles CAT and DOG are similar Example 1: The triangles CAT and DOG are similar. The larger triangle is an enlargement of the smaller triangle. How long is side GO? T G 2 cm ? cm 1.5 cm A 3 cm O C 3 cm 6 cm D Each side and its enlargement form a pair of sides called corresponding sides. Length of corresponding sides GD=3 TC=1.5 DO=6 CA=3 GO=? TA=2 Ratio of Lengths 3/1.5=2 6/3=2 ?/2=2 (1) Corresponding side of TC --> GD (2) Corresponding side of CA--> The scale factor is 1:2. DO (3) Corresponding side of TA--> GO GO is 4 cm.

Using Proportions in Poster Design You have been asked to create a poster. You have a 3.5 inch by 5 inch photo that you want to enlarge. You want the enlargement to be 16 inches wide. How long will it be? 5 3.5 x Remember, mean different things 16

One more thing….. If two polygons are similar, then the ratio of their perimeters is equal to the ratios of their corresponding side lengths. So the perimeter of ABCD is 22 and the perimeter of EFGH is 11. Also, a scale factor of 2:1!!