This Question is from chapter Quadrilaterals. EXPERTS, PLEASE ANSWER THIS AS SOON AS POSSIBLE

If APB and CQD are two parallel lines then find the type of quadrilateral formed by the bisectors of the angles APQ, CPQ, QCP, and PQD.

Asked by prakash.sanyasi | 31st Oct, 2019, 11:27: PM

Expert Answer:

The question should be:
If APB and CQD are two parallel lines then find the type of quadrilateral formed by the bisectors of the angles APQ, BPQ, CQP, and PQD
L e t space X space a n d space Y space b e space t h e space i n t e r s e c t i o n space o f space b i s e c t o r s space o f space a n g l e s space A P Q comma space C Q P space a n d space a n g l e s space B P Q comma space P Q D space r e s p e c t i v e l y
G i v e n colon space A P B space vertical line vertical line space C Q D
rightwards double arrow angle A P Q equals angle P Q D space.... space A l t e r n a t e space a n g l e s
rightwards double arrow angle X P Q equals angle P Q Y
therefore space P X space vertical line vertical line space Q Y
S I m i l a r l y comma space angle Q P Y equals angle P Q X
therefore space Q X space vertical line vertical line space P Y
therefore space P X Q Y space i s space a space p a r a l l e log r a m
C Q D space i s space a space l i n e
rightwards double arrow angle C Q P plus angle P Q D equals 180 degree
rightwards double arrow 2 angle P Q X plus 2 angle P Q Y equals 180 degree
rightwards double arrow angle P Q X plus angle P Q Y equals 90 degree
rightwards double arrow angle X Q Y equals 90 degree
therefore space angle X P Y equals 90 degree
rightwards double arrow space angle P X Q equals 90 degree space a n d space angle P Y Q equals 90 degree
H e n c e comma space P X Q Y space i s space a space r e c tan g l e.

Answered by Renu Varma | 1st Nov, 2019, 10:19: AM