practice problems pending

Q1.


S1.
QR || AC by MPT.
=> line BHE is perpendicular to QR.
In triangle AHB, using MPT, QP || BH.
=> QR is perpendicular to QP => angle PQR = 90
H.P.

Q2.

ABCD is a quadrilateral in which AB = AD.

The bisectors of ∠BAC and ∠CAD intersect the sides BC and CD at E and F, respectively.

Prove that (EF ||BD).


S2.
Using Angle bisector theorem:

Triangle ABC:
AB/BE = AC/EC

Triangle ADC:
AD/DF = AC/FC

=> AB/AC = BE/EC = AD/AC = DF/FC (since AB = AD)
Now in triangle BDC:
EF divides the sides BC and DC in same ratio
=> EF || BD
H.P.


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