give a detailed proof(with reasons) for AAA / AA similarity criterion.

Asked by  | 13th Feb, 2010, 07:33: PM

Expert Answer:

 

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.

Regards,

Team,

TopperLearning.

 

Answered by  | 14th Feb, 2010, 07:13: AM

Queries asked on Sunday & after 7pm from Monday to Saturday will be answered after 12pm the next working day.