# ​​in triangle abc , x is the middle point of ac . if xy is parallel to ab then prove that y is the mid point of ab

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Please find below the solution to the asked query:

Correct query : ​​In triangle ABC , X is the middle point of AC . if XY is parallel to AB then prove that Y is the mid point of BC .

From given information we form our diagram , As :

Here , AX =  CX = $\frac{\mathrm{AC}}{2}$                                                                  --- ( 1 )
And

XY | |  AB

From BPT we get in triangle ABC

Therefore,

From above equation we can say that " Y is mid poin of line BC "                                        ( Hence proved )

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• 4
pls give the answer with the figure

• -2
the question is abit wrong . it should be prove that y is the midpoint of bc
Sorry the image can't be uploaded. But don't fret . follow  the steps to draw the image
step1: draw a triangle ABC
step2: mark points x and y on ac and bc respectively

solution:
given: ABC is a triangle. x and y are points on ac and bc respectively. xy is parallel to ab. x is the midpoint of ac.
to prove : y is the midpoint of BC

Proof:
X is the midpoint of AC    [Given]
therefore, AX=XC
​                 XA=CX
XY parallel to AB     [Given]
CX/XA=CY/YB   [Basic Proportionality Theorem]
as we know XA=CX
​XA/XA= CY/YB
1=CY/YB
​YB=CY

now, YB+CY=BC
But YB=CY  [Proved above]
YB+YB=BC
2YB=BC
YB=BC/2
Hence Y is the midpoint of BC
as we know

• -1
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