AD and BC are equal perpendiculars to a line segment AB (see figure).

1.	AD and BC are equal perpendiculars to a line segment AB (see figure). Show that CD bisects AB.
Answer» ⠀⠀ıllıllı uoᴉʇnloS ıllıllı $\setlength{\unitlength}{1.0 cm}}\begin{picture}(12,4)\thicklines\put(1,1){\line(1,0){6.5}}\put(1,1.1){\line(1,0){6.5}}\end{picture}$ In ∆BOC and ∆AOD, We have: ∠BOC = ∠AOD BC = AD [Given] ∠BOC = ∠AOD [Vertically opposite angles] ∴ ∆OBC ≅ ∆OAD [By AAS CONGRUENCY] ➠ OB = OA [By C.P.C.T.] i.e., O is the mid-point of AB. Thus, CD bisects AB. $\setlength{\unitlength}{1.0 cm}}\begin{picture}(12,4)\thicklines\put(1,1){\line(1,0){6.5}}\put(1,1.1){\line(1,0){6.5}}\end{picture}$

AD and BC are equal perpendiculars to a line segment AB (see figure). Show that CD bisects AB.

Answer»

$\setlength{\unitlength}{1.0 cm}}\begin{picture}(12,4)\thicklines\put(1,1){\line(1,0){6.5}}\put(1,1.1){\line(1,0){6.5}}\end{picture}$

In ∆BOC and ∆AOD, We have:

∠BOC = ∠AOD

BC = AD [Given]

∠BOC = ∠AOD [Vertically opposite angles]

∴ ∆OBC ≅ ∆OAD [By AAS CONGRUENCY]

➠ OB = OA [By C.P.C.T.]

i.e., O is the mid-point of AB.

$\setlength{\unitlength}{1.0 cm}}\begin{picture}(12,4)\thicklines\put(1,1){\line(1,0){6.5}}\put(1,1.1){\line(1,0){6.5}}\end{picture}$