Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion . In other words, similar triangles are the same shape, but not necessarily the same size. The triangles are congruent if, in addition to this, their corresponding sides are of equal length. The side lengths of two similar triangles are proportional. That is, if Δ U V W is similar to Δ X Y Z , then the following equation holds: U V X Y = U W X Z = V W Y Z This common ratio is called the scale factor . The symbol ∼ is used to indicate similarity.
Example: Δ U V W ∼ Δ X Y Z . If U V = 3 , V W = 4 , U W = 5 and X Y = 12 , find X Z and Y Z . Draw a figure to help yourself visualize.
Write out the proportion. Make sure you have the corresponding sides right. 3 12 = 5 X Z = 4 Y Z The scale factor here is 3 12 = 1 4 . Solving these equations gives X Z = 20 and Y Z = 16 . The concepts of similarity and scale factor can be extended to other figures besides triangles. Naiomi M. Is the answer to this 9:25 ratio? Is that right? how do I solve it? 1 Expert AnswerThe ratio of corresponding sides of similar triangles is 3 : 5; then Find the ratio of their areas. According to theorem of areas of similar triangles "When two triangles are similar, the ratio of areas of those triangles is equal to the ratio of the squares of their corresponding sides". \[= \frac{3^2}{5^2}\] \[= \frac{9}{25}\] Concept: Areas of Two Similar Triangles Is there an error in this question or solution? |