in the goven figure, ABCD is a parallogram and line segments AX and CY bisects anglesA and C respectively... Show that AX || CY....
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Given : ABCD is parallelogram and AX and CY are angle bisectors.
To Prove : AX || CY
Proof : Since ABCD is parallelogram so its opp. angles are equal.
< A = < C
1 < A / 2 = 1 < C / 2
< 1 = < 3 __(1)
Since AB || CD
< 2 = < 3 [ Alternate angles ] __(2)
From 1 and 2 we get
< 1 = < 2
Hence, AY is transversal for such two lines AX and CY who corresponding angles are equal and hece AX || CY.
Q.E.D
Have great future ahead!
Given : ABCD is parallelogram and AX and CY are angle bisectors.
To Prove : AX || CY
Proof : Since ABCD is parallelogram so its opp. angles are equal.
< A = < C
1 < A / 2 = 1 < C / 2
< 1 = < 3 __(1)
Since AB || CD
< 2 = < 3 [ Alternate angles ] __(2)
From 1 and 2 we get
< 1 = < 2
Hence, AY is transversal for such two lines AX and CY who corresponding angles are equal and hece AX || CY.
Q.E.D
Have great future ahead!
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