Criteria for similarity of triangles
- CBSE · NCERT Class 10, Ch 6 Triangles
The criteria for similarity are the tests that prove two triangles similar: AAA or AA, SSS and SAS.
To show two triangles are similar, you do not need to check every angle and every side. One of these tests is enough:
- AA (or AAA): two angles of one triangle equal two angles of the other. The third pair is then equal too, since the angles of a triangle add up to 180°.
- SSS: all three pairs of sides are in the same ratio.
- SAS: one angle is equal, and the two sides that form it are in the same ratio.
A small example
In trapezium ABCD, AB ∥ DC and the diagonals meet at O. In ∆AOB and ∆COD, ∠OAB = ∠OCD and ∠OBA = ∠ODC, as alternate interior angles. So ∆AOB ∼ ∆COD by AA. This gives AO/CO = BO/DO.
Where marks go
This is Question 22(A) of CBSE's 2026-27 Maths Standard sample paper, worth 2 marks. The board's Maths Standard marking scheme for 2026-27 gives 1 mark for the two pairs of equal angles, with the reason: alternate interior angles. Half a mark is for the similarity statement, with the criterion named. The last half mark is for the ratio.
So naming the criterion is written into the scheme. So is the reason each pair of angles is equal. An answer that jumps from the figure to the ratio shows neither step. Read more on how step marking works.
Sources
Facts last checked against these sources on 30 September 2026.
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