12. ABCD is a trapezium in which AB || CD and AD = BC (see Fig).Show that 01) ∠A = ∠B 02) ∠C = ∠D 03) ∆ABC = ∆BAD 04) diagonal AC = diagonal BD {विकर्ण AC = विकर्ण BD है}।

12. ABCD is a trapezium in which AB || CD and AD = BC (see Fig).

Show that

12. ABCD एक समलंब है, जिसमें AB || DC और AD = BC है (देखिए आकृति)

दर्शाइए कि

01) ∠A = ∠B

02)  ∠C = ∠D

03) ∆ABC = ∆BAD

04) diagonal AC = diagonal BD

विकर्ण AC = विकर्ण BD है।

Sol.

सिद्ध करना है : 

(i)  ∠A = ∠B

 

Construction:

AD || CE

then AD = CE & AE = DC

In ∆CBE

   BC = CE

   ∠B = ∠E

∠ABC + ∠CBE = 18° [L.P.].......(i)

∠DAE + ∠AEC = 180° [ASSOTRS]

∠DAE + ∠AEC = 180° 

∠DAE + ∠CBE = 180° ............(ii)

From equation (i) and (ii)

∠DAC + ∠CBE =  ∠ABC+ ∠CBE 

∠DAC = ∠ABC

∠A = ∠B.             Proved (i)

All BC & AB is turonsoul

fill LA+·LD = 1R₁" (POSOTRY) - ADII BC & CDs Trouval D LBtLc = 185 (ASSOTRS).

Spiral