In the given figure, T and M are two points inside a parallelogram PQRS such that PT = MR and PT || MR. Then prove that RT || PM
and RT = RM
1 answer:
We have been given a parallelogram PQRS and T and M are two points inside it.
Given also that PT = MR and PT || MR. ----- (1)
Join RT and PM.
Now, in the quadrilateral PMRT, one pair of opposite sides are parallel and equal from (1)
Therefore, PMRT is a parallelogram.
By the properties of parallelogram, the other pair of opposite sides are too parallel and equal.
Hence, RT || PM and RT = PM.
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Okay so I attatched pictures of my work. I would just graph it by plugging in x-values on either side of the vertex into the equation. For example, the vertex is at (-2,3). So try plugging x=-5 and x=1 into the equation (y=a(x-h)^2 +k).
y=(x+2)^2 +3
y=((1)+2)^2 +3=(3)^2+3= 9+3= 12
Now you can plot the vertex (-2,3), the point (1,12), and (-5,12). From there just connect the dots and you should get a graph that looks similar to the last picture I attached. Hope this all made sense sorry it was so wordy I just wasn't sure how much you knew or didn't know. So, I thought it would be better to explain it all rather than not enough.
y=(x+2)^2 +3
y=((1)+2)^2 +3=(3)^2+3= 9+3= 12
Now you can plot the vertex (-2,3), the point (1,12), and (-5,12). From there just connect the dots and you should get a graph that looks similar to the last picture I attached. Hope this all made sense sorry it was so wordy I just wasn't sure how much you knew or didn't know. So, I thought it would be better to explain it all rather than not enough.