Step-by-step explanation:
here, ABCD is a Parallelogram, E and F are the mid-points of sides AB and CD respectively.
Therefore, AB║EF║BC
The line PQ intersects the line segments AD, EF and BC at P, O and Q respectively.
We need to prove that PO = OQ.
Now, If three or more parallel lines intersect a transversal, then they cut off the transversal proportionally.
here, AD, EF and BC are three parallel lines and PQ is the transversal.
∴
Since E and F are mid-points of AB and CD respectively, we have,
AE = EB and CF = DF
⇒
⇒ PO = OQ proved.
hope it will help you.
Answer:
PO
----- = 1
OQ
I hope it's help you
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Answers & Comments
Step-by-step explanation:
here, ABCD is a Parallelogram, E and F are the mid-points of sides AB and CD respectively.
Therefore, AB║EF║BC
The line PQ intersects the line segments AD, EF and BC at P, O and Q respectively.
We need to prove that PO = OQ.
Now, If three or more parallel lines intersect a transversal, then they cut off the transversal proportionally.
here, AD, EF and BC are three parallel lines and PQ is the transversal.
∴![\frac{AE}{EB} = \frac{CF}{DF} = \frac{PO}{OQ} \frac{AE}{EB} = \frac{CF}{DF} = \frac{PO}{OQ}](https://tex.z-dn.net/?f=%5Cfrac%7BAE%7D%7BEB%7D%20%3D%20%5Cfrac%7BCF%7D%7BDF%7D%20%3D%20%5Cfrac%7BPO%7D%7BOQ%7D)
Since E and F are mid-points of AB and CD respectively, we have,
AE = EB and CF = DF
⇒![\frac{PO}{OQ} = 1 \frac{PO}{OQ} = 1](https://tex.z-dn.net/?f=%5Cfrac%7BPO%7D%7BOQ%7D%20%3D%201)
⇒ PO = OQ proved.
hope it will help you.
Answer:
PO
----- = 1
OQ
Step-by-step explanation:
I hope it's help you