Question

in figure,points A and B are on the same side of a line.ADperpendicular and BE perpendicular at D and E respectively.if C is the mid point of AB. PROVE THAT CD=CE


FIGURE IS A SHOWN.....PLZ ANSWER IT....ITS MY PROMISE I WILL SELECT U A BRAINLIEST ONE THNX....PLZ BE FAST

Answer 1

Hello friend,

Here, AD is perpendicular to l, CF is perpendicular to l and BE is perpendicular to l
AD || CF || BE
In Triangle 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 Triangle 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 Triangles CDF and CEF
DF = EF (F is the mid-point of DE)
CF = CF (common)
Angle CFD = Angle CFE (Each 90 degrees since F is perpendicular to l)
∴ DDF is congruent to DCEF (SAS congruence criterion)
=> CD = CE (C.P.C.T)
Hence proved.

You can take help of the diagram given below :)