At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
Write a proof to show that the diagonals of a parallelogram bisect one another. Be sure to create and name the appropriate geometric figures. This figure does not need to be submitted.
How many steps do they want?
Hmmm... well, this is going to be hard. o-o
Ok, so step one. What are we given.
Let's make a parrallelogram ABCD. |dw:1450384929769:dw| What do we KNOW right away about this figure?
i found something
Ok, so what do we know about parallelogram ABCD?
diagonals of a parallelogram bisect one another?
That's what we're trying to prove.
Well, if it's a parallelogram, we know that AB and CD are parallel and same with AC and BD
Ugh... hold on a second. @AlexandervonHumboldt2 Can you help me, Shurik?
shuriks here shurik's looking
Lol, so what would the next step be? Given AB and CD are parallel.
omg lol you are amazing at proofs. I can only do it with guides =[
Ok, so let me try to write this out.
is that it?
as AB=CD, angle ABP=angle DCP and angle APB=angleCPD triangles are congruent
thus corresponding sides are congruent
thus AP=PD do the same with other pair of triangles
Given: AB and CD are congruent and parallel Given: AC and DB are congruent and parallel Vertical Angles Theorem:
I will never be good at proofs ='[
@12G got the concept?
i got lost imma reread that again
AB=CD, angle ABP=angle DCP and angle APB=angleCPD triangles are congruent. corresponding sides are congruent
is that good
in the end add that they bisect and that AP=.....
AP=PD that ?