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Similar triangle:Two triangles are similar if their corresponding sides are all in the same proportion in length and corresponding angles are same in measure.
In the above figure, \(ΔPQR\) and \(ΔP'Q'R'\) have the same size and different shape. They are similar. This can be expressed as \(ΔPQR ~ ΔP'Q'R'\).
Important!
Corresponding vertices: \(P\) and \(P'\), \(Q\) and \(Q'\), and \(R\) and \(R'\).
Corresponding sides: \(\frac{PQ}{P'Q'}\), \(\frac{QR}{Q'R'}\), \(\frac{RP}{R'P'}\).
Corresponding angles: \(∠P\) and \(∠P'\), \(∠Q\) and \(∠Q'\), and \(∠R\) and \(∠R'\).
Corresponding sides: \(\frac{PQ}{P'Q'}\), \(\frac{QR}{Q'R'}\), \(\frac{RP}{R'P'}\).
Corresponding angles: \(∠P\) and \(∠P'\), \(∠Q\) and \(∠Q'\), and \(∠R\) and \(∠R'\).
Let us discuss the different types in the similar triangles. They are:
- SSS similarity
- ASA similarity
SSS similarity: The three sides of one triangle are in the same proportion to the three sides of another triangle.
Example:
In here, the three sides of the first triangle are \(11\) units, \(13.9\) units and \(17.3\) units which is similar to the second triangle whose sides are the same proportion \(5.5\) units, \(7\) units and \(8.7\) units respectively.
Important!
SSS stands for "side, side, side" it means that we have two triangles with all three sides has same proportion.
SAS similarity:Two sides of one triangle are same proportion to the corresponding sides of another triangle and the included angle of one triangle are equal to the angle of another triangle, and then the triangles are similar.
Example:
In here the two sides of the first triangle are \(17\) units and \(16\) units, and the included angle is \(57°\) which is similar to the second triangle whose sides are the same proportion \(8.5\) units and \(8\) units with the included angle are equal \(57°\).
Important!
SAS stands for "side, angle, side" and means that we have two triangles with two sides has same proportion and one angle are equal.
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