Question

ABCD is a rhombus rabs is a straight line such that RA=AB=BS prove that RD AND SC when produced Meet at right angles

Answer 1

Answer:

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Step-by-step explanation:

We know that the diagonals of a rhombus are perpendicular bisector of each other.

∴OA=OC,OB=OD,∠AOD=∠COD=90

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and, ∠AOB=∠COB=90

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In ΔBDE, A and O are mid - points of BE and

BD respectively.

∴OA∥DE

⇒OC∥DG

In ΔCFA,B and O are mid - points AF and AC respectively

∴OB∥CF

⇒OD∥GC

Thus, in quadrilateral DOCG, we have

OC∥DG and OD∥GC

⇒DOCG is a parallelogram.

∴∠DGC=∠DOC

⇒∠DGC=90

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