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Question 899843: 1. Prove analytically that the diagonals of a parallelogram bisect each other.
2. What are the lengths of the segments into which the y-axis divides the segment joining (-6,-6) and (3,6).
Pls explain every detail I'm slow. Thank you!
Answer by MathLover1(20850)   (Show Source):
You can put this solution on YOUR website! 1.
Proof
Let the two diagonals be AC and BD and O be the intersection point.
We have to prove that O is the midpoint of AC and also the midpoint of BD.
Hence,  and 
We will prove using congruent triangles concept.
Consider two Triangles ABO and COD.
1.  ....( Line AC is a transversal of the parallel lines AB and CD, hence alternate angles).
2.  ....(Line BD is a transversal of the parallel lines AB and CD, hence alternate angles).
3.  ....(Opposite angles when two lines intersect each other area equal)
From conditions 1,2 and 3
Triangle ABO is similar to triangle CDO (By Angle -Angle similar property)
Since Triangles are similar, Hence ratio of sides are equal from similar triangles property.
 .........(4)
From theorem that Opposite sides of a parallelogram are equal,
 ..........(5)
From equation (4) and (5)
Similarly, 
Hence, we conclude that AO = CO and BO = DO.
Lesson (Proof: The diagonals of parallelogram bisect each other) was created by tutor chillaks.
2.
what are the lengths of the segments into which the y-axis divides the segment joining ( ,) and ( , ) ?
 means 
Let the ratio be  :1
The 
=> 
=>  =>;
Hence 
Hence intersection point is C ( , )
Hence Length A (,) to C (,) = units
Length C (,) to B (,) = units
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