Given that ABCD is a parallelogram with diagonals intersecting at M. Segment PQ is drawn such that P lies on AB and Q lies on DC and it passes through M. Prove that PM is congruent to QM.

we thus have enough informnation to prove that the two triangles are congruent. Because of thism, one side of the triangles, Pm which is the congruent side to that of PQ must be equal as well and

PM = QM

Step-by-step explanation:

because it's a parrallelogram, Ad = BC and AB = DC.

P passes through both  AB and DC on a diagonal, angles created by P have oppoiste exterior angles of eachother.

the diagonals of AC create congruent angles at DMC and AMB and because P is cutting through them, the angles P cuts at DMQ and QMC are equal to that of AMP and PMB

that being said, we now see that the angles of APM triangle and AMC triangol are equal and because the diagonal of BD is is being cut by AC, which AD is parralel to BC  and AB to Dc, we know now that lines AM and MC are congruent

we thus have enough informnation to prove that the two triangles are congruent. Because of thism, one side of the triangles, Pm which is the congruent side to that of PQ must be equal as well and

thus PM = QM

to plot points   for x just start at the origin (middle) and go to the left however many times it say(if the number is a positive) if the number is a negative then go right however many times it says if it is 0 go nowhere

now keep you pencil there and go up however many times it says on y(if it is positive) if it is negative then go down however many times it says. if it says 0 go nowhere.

you have just plotted a point! now when you finish plotting all of them connect them with a ruler

plot each point as (-3, 7), (0,4), (3,1), (8,-4)   in the parenthesis on the left of the comma is x and the right is y.

step-by-step explanation:

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