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3CD TH चतुर्ुज है। जिसमें AB||DC और 200 न 80 तो _ चित्र 9.23D एक समान्तर चतुर्मुज है। ? और 0 क्रमशः सम्पुन भुजाओंकीजिए कि 1२९५ एक समान्तर चतुर्मुज है ।c %u,fl’bचित्र 9.2428 और 00 केकि०. |
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Answer» See diagram. You can see a general quadrilateral with AB || DC and AD = BC. Extend the sides AD and BC till E and F as shown. As AB and CD are two parallel lines and AD intersects them both, the angles D and EAB are same. But angle EAB = 180 - A. so, angleD = 180 - A Similarly, the line BC intersects parallel lines AB and DC, so angle C = angle FBA = 180 - B Now, draw perpendiculars from D and C onto AB meeting AB at G and H respectively. Since AB || DC, the sides DG || CH. Also, DG = CH = distance between the parallel lines. Looking at the triangles DGA and CHB, we find that DG = CH, AD = BC (given), angle G = angle H = 90°.ΔDGA andΔCHB are congruent. Hence angleA = angleB. 2In quadrilateral PSQR, SP || QR (SP is a part of DP and QR is a part of QB) Similarly, SQ || PR So, PSQR is a parallelogram |
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