Two figures are said to be similar if they have similar shape but size may or may not be equal. As we have studied in class 9 that if both shape and size of both figures are same then they are said to be congruent figures.
Examples of similar figures:
Also, Two polygons with the same number of sides are similar, if
Remember, The ratio of corresponding sides of a polygon is referred as the scale factor or representative fraction.
The same rule which is applied on similarity of polygon is done with it.
Two triangles are similar, if
(i) Their corresponding angles are equal and
(ii) Their corresponding sides are in the same ratio (or proportion).
Geometrically:
∠A = ∠D, ∠B = ∠E, ∠C = ∠F
Then the two triangles will be similar.
The ratio of any two corresponding sides in two equiangular triangles is always same.
Q1: In the given figure, If PQ  RS, prove that ∆POQ ~ ∆SOR.
Solution:
PQ  RS (Given)
So, ∠P = ∠S (Alternate angles)
And, ∠Q = ∠R
∠POQ = ∠SOR (Vertically opposite angles)
Thus, ∆POQ ~ ∆SOR (AAA similarity rule)
Q2: In the given figure, if OA .OB = OC .OD. Show that ∠A = ∠C and ∠B = ∠D.
Solution:
Given that,
OA .OB = OC .OD
Also, ∠AOD = ∠COB (vertically opposite angles) …..(ii)
From (i) and (ii)
∆AOD ~ ∆COB …. (SAS similarity rule)
Thus, ∠A = ∠C and ∠B = ∠D.
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