CBSE Class 10 Answered
Consider the two triangles, and the angles be denoted by capital letters and length of side opposite to the angle by same but lower case letter.
sin C = AD/b and sinB = AD/c ....................... AD BC
AD = b sinC = c sinB
sinB/b = sinC/c
Similarly if we draw a perpendicular from B onto AC, use the same reasoning, we find,
sinC/c = sinA/a
Therefore we obtain the sine rule,
sinA/a = sinB/b = sinC/c .....................(1)
Also in PQR,
sinP/p = sinQ/q = sinR/r .....................(2)
But the corresponding angles in the two traingles are equal is our assumption.
So we can write using (1) and (2), by taking the ratio,
a/p = b/q = c/r
which shows that the two triangles are similar.
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