SOLUTION: 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) an

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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