SIMILAR SHAPES
CONTENT
- Scale Factor in Calculating Lengths (Ratio of Corresponding Shapes)
- Determining Similarity
- Area and Volume of Similar Shapes
Scale Factor in Calculating Lengths (Ratio of Corresponding Shapes)
If two triangles are similar, then, we can say that one is the scale drawing of the other (i.e. one is an enlargement of the other)
Let there be a pair of similar shapes, where side AB correspond to PQ, and there exist a scale factor K,
Then, \(AB × K = PQ\)
Or \(PQ × K = AB\)
Consider the diagrams below.
The rectangles below are similar.
Find the scale factor of enlargement that maps A to B.
The rectangles below are similar.
Find the scale factor of enlargement that maps A to B.
If the above triangles are similar, the following should be noted,
- Side AB correspond to side AC in the ratio 4.2 to 6.3 i. e 4.2 : 6.3
- Side BE correspond to side CD in the ratio 4.8 to 7.2
- Side EA correspond to side DA in the ratio 6 to 9
Therefore,
\(\frac{AB}{AC} = \frac{BE}{CD} = \frac{EA}{DA}\)
→ \(\frac{4.2}{6.3} = \frac{4.8}{7.2} = \frac{6}{9} = \frac{2}{3}\)
Therefore, the ratio of triangle ABE to triangle ACD is 2:3
If we are told that two objects are similar and we can find the scale factor of enlargement by comparing corresponding sides, then we can calculate the value of an unknown side.
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