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CBSE Class 9 Answered

ABCD is a parallelogram and the line segement AX and CY bisect angle A and angle C respectively. prove that AX\\ CY  
Asked by 156853855216010 | 15 Aug, 2018, 08:10: PM
answered-by-expert Expert Answer
begin mathsize 16px style Given colon space
ABCD space is space straight a space parallelogram.
rightwards double arrow angle straight A space equals space angle straight C space left parenthesis space opposite space angles space of space straight a space parallelogram space are space equal right parenthesis
rightwards double arrow 1 half angle straight A space equals space 1 half angle straight C
rightwards double arrow angle 1 space equals space angle 2 space space space space.... left parenthesis straight i right parenthesis space space space
left parenthesis since comma space AX space is space straight a space bisector space of space angle straight A space and space CY space is space straight a space bisector space of space angle straight C right parenthesis
Now comma space AB space parallel to space CD space and space CY space is space the space transversal.
rightwards double arrow angle 2 space equals space angle 3 space space space.... left parenthesis ii right parenthesis space space space space space...... space alterante space interior space angles
From space left parenthesis straight i right parenthesis space and space left parenthesis ii right parenthesis comma space we space get
angle 1 space equals space angle 3
rightwards double arrow Transversal space AB space intersects space AX space and space CY space at space straight A space and space straight Y space respectively space
such space that space space space angle 1 space equals space angle 3
straight i. straight e comma space corresponding space angles space formed space are space equal.
rightwards double arrow AX space parallel to space CY
end style
Answered by Yasmeen Khan | 16 Aug, 2018, 12:22: PM
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