Question

prove that the bisectors of opposite angles a parallelogram are parallel

Answer 1

In the given figure we have DL parallel to BM and BL and DM are two transversals then,

∠DLB + ∠LBM = 180° and ∠LDM + ∠DMB = 180°

⇒ ∠DLB = 180° - ∠LBM and

∠DMB = 180° - ∠LDM  .... (3)

As proved earlier ∠LBM = ∠LDM

Therefore, ∠DLB = 180° - ∠LDM  ... (4)

Now, on comparing (3) and (4), we get

∠DMB = ∠DLB

Therefore, LDMB is a parallelogram as its opposite angles are equal.

∴ BL || DM

 

Answer 2

In this picture , ABCD is a parallelogram in which

AX and CY bisects opposite angle A and angle B respectively .


It has also been proved that these two bisectors are parallel .

Hope that it will be useful for you ....

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