Similar Figures

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Mathematics Geometry Similar Figures

	Similar Figures
	Similar figures have the same shape (but not necessarily the same size) and the following properties: ? Corresponding sides are proportional. That is, the ratios of the corresponding sides are equal. ? Corresponding angles are equal For example, consider the following squares. Clearly, Also A=P B=Q C=R D=S Thus the squares are similar figures as their corresponding sides are proportional and their corresponding angles are equal. [Note: Each side of figure PQRS has been multiplied by 2 to obtain the sides of figure ABCD. The number 2 is called the scale factor. Similar figures are equiangular (i.e. the corresponding angles of similar figures are equal). ] Similar Triangles: Similar triangles can be applied to solve real world problems. For example, similar triangles can be used to find the height of a building, the width of a river, the height of a tree etc. If two triangles are similar, then: ? they are equiangular ? the corresponding sides are in the same ratio ? the angle included between any two sides of one triangle is equal to the angle included between the corresponding sides of the other triangle Example: Find the value of the pronumeral in the following diagram. Solution: ? ABC and ? ADE are similar as they are equiangular. x + 4 = 2x or x = 4