Question

A and B are two points on the same side of line ' l '. AD and BE are perpendicular on line l intersecting D and E respectively. c is the midpoint of AB. Prove that CD=CE

Answer 1

hey !!!

Here is the answer to your query.
_____________
 

The given information can be represented graphically as

( Refer pic for it )

 

Here, AD ⊥ l, CF ⊥ l and BE ⊥ l

AD || CF || BE

In ∆ABE, CG || BE  (CF || BE)

And C is the mid-point of AB

Thus, by converse mid-point theorem, G is the mid-point of AE

 

In ∆ADE, G is the mid-point of AE and GF || AD  (CF || AD) 

Thus, the converse of mid-point theorem, F is the mid-point of DE.

 

In ∆CDF and ∆CEF

DF = EF  (F is the mid-point of DE)

CF = CF  (common)

∠CFD = ∠CFE   (Each 90° since F ⊥ l)

∴ DDF ≅ DCEF  (SAS congruence criterion)

⇒ CD = CE  (C.P.C.T)

Hence proved

 _______________

Hope! This will help you.

Cheers!

 # Nikky