Question

if bisector of angles of quadrilateral encloses a rectangle then show that it is a parallelogram
plz tell​

Answer 1

Answer:

If the bisectors of angles of a quadrilateral enclose a rectangle, then show that it is a parallelogram. 2. L, M, N, K are mid-points of sides BC, CD, DA and AB respectively of square ABCD, prove that DL, DK, BM and BN enclose a rhombus.

Step-by-step explanation:

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Answer 2

Answer:

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Step-by-step explanation:

Quadrilateral PQRS has angle bisectors PT,QA,RA,SC.

ΔPQB,ΔQBT,ΔSDC are right angled triangle.

Let angle P=2x

so, ∠PQB=90−x=∠BQT

∴∠QTB=(90−(90−x))=x

∠CTR=180−x

In triangle SDR,

∠RDS=90∘

, in parallelogram DCTR

∠DCT & ∠CDR=90∘

∴∠DRT=x & ∠DRS=x

∴∠DSR=90−x

sum of adjacent angles, ∠P+∠Q=180∘

Opposite angles ∠P=∠R,∠Q=∠C

∴ PQRS is parallelogram