If two parallel lines are intersected by a transversal line prove (the bisector of the two pair of interior angles enclose a rectangle
Answers
Answer:
AB and CD are two parallel line intersected by a transverse L
X and Y are the point of intersection of L with AB and CD respectively.
XP, XQ, YP and YQ are the angle bisector of ∠AXY,∠BXY,∠CYXand∠DYX
AB∥CD and L is transversal.
∴∠AXY=∠DYX (pair of alternate angle)
⇒
2
1
∠AXY=
2
1
∠DXY
⇒∠1=∠4(∠1=
2
1
∠AXYand∠4=
2
1
∠DXY)
⇒
YQ
PX
(If a transversal intersect two line in such a way that a pair of alternate
interior angle are equal, then the two line are parallel)
(1)
Also ∠BXY=∠CYX (pair of alternate angle)
⇒
2
1
∠BXY=
2
1
∠CYX
⇒∠2=∠3(∠2=
2
1
∠BXYand∠3=
2
1
∠CYX)
⇒
XQ
PY
(If a transversal intersect two line in such a way that a pair of alternate
interior angle are angle, then two line are parallel)
(2)
from (1) and (2), we get
PXQY is parallelogram ....(3)
∠CYD=180
0
⇒
2
1
∠CYD=
2
180
=90
0
⇒
2
1
(∠CYX+∠DYX)=90
0
⇒
2
1
∠CYX+
2
1
∠DYX=90
0
⇒∠3+∠4=90
0
⇒∠PYQ=90
0
.......(4)
So using (3) and (4) we conclude that PXQY is a rectangle.
Hence proved.
hope it helped you
i had attached the images of the text also to help you more
plz mark brainliest
