Prove that Triangle ABC is Similar to Triangle PQR
Asked by ANKUR123 | 3rd Aug, 2008, 11:41: AM
You need to do a construction here: Produce AD to E such that AD = De and produce PM to N such that PM = MN. Now join BE, CE, QN , RN.
The two quadrilaterals formed will be parallelograms because diagonals bisect.
Now consider Triangles ABE and PQN.
AC = BE and PR = QN. AE = 2 AD and PN = 2 PM.
So, AB/PQ = BE/ QN = AE / PN
So Triangles ABE and PQN are similar
So angle BAE = angle QPN ...(1)
similarly angle CAE = angle RPN...(2)
Adding (1) and (2) , we get
angle BAN = angle QPR .
Now by SAS similarity condition
triangle ABC is similar to triangle to triangle PQR.
Answered by | 26th Sep, 2008, 01:53: PM
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