Similar Figures

Similar figures. Figures with same shape. They are not necessarily the same size.

Two polygons are similar if their corresponding angles are congruent and the measures of their corresponding sides are in proportion (scale factor).

“~” is the sign for “is similar to”.

Polygons can still be similar even if one of them is rotated, example:

Essential Question:
If a polygon is enlarged or reduced, which parts changes and which parts remains the same?

Vocabulary:

Similar
Congruent
Enlarged
Reduced
Scale factor

Examples:

Triangles EFG and QRS are similar. The length of the sides of EFG are 3, 4, and 5. The length of the smallest side of QRS is 7.5, what is the length of the longest side of QRS?

(All units in the examples are in centimeters)

Triangles EFG and QRS are similar. The length of the sides of EFG are 3, 4, and 5. The length of the smallest side of QRS is 7.5, what is the scale factor?

Two triangles are similar if one of them is larger than the other by a Scale Factor.

Triangles EFG and QRS are similar. The length of the sides of EFG are 3, 4, and 5. The length of the smallest side of QRS is 7.5, what is the perimeter of QRS?

Perimeter of triangle EFG = 3+4+5 = 12

A scale factor is simply a number that multiplies the dimensions of a shape.

Perimeter of triangle QRS = 2.5 (3+4+5) = (7.5 + 10 + 12.5) = 30

Triangles EFG and QRS are similar. Find the corresponding sides