Q13 of 24 Page 157

In a triangle ABC, D is the midpoint of the side BC; through the point A, PQ is any straight line. The perpendiculars from the points B, C and D on PQ are BL, CM and DN respectively; let us prove that, DL = DM.


Since BL||DN||CM and D is midpoint of BC, by using the theorem:-


If three or more parallel straight lines make equal intercepts from a traversal, then they will make equal intercepts from another traversal.


⇒ LN = MN


In ΔDLN and ΔDMN,


DN = DN (common)


∠DNL = ∠DNM = 90° (given)


LN = MN (proved above)


∴ ΔDLN ≅ ΔDMN by SAS congruency.


As a result of it, DL = DM


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