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# Geometry Proof

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Two line segments, AB and CD, bisect one another at point 0. Prove that the lines AC and BD are parallel.

Sep 19, 2018
edited by FreezingTNT  Sep 19, 2018
edited by FreezingTNT  Sep 19, 2018

### 1+0 Answers

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Two line segments, AB and CD, bisect one another at point 0. Prove that the lines AC and BD are parallel.

I suggest you start with the diagram.

Consider triangles OAC and  OBD

OA=OB  Since 0 bisects AB

OC=OD  since o bisects CD

angleBOD=angleAOC     Vertically opposite angles

therefore

triangle OAC is congruent to triangle OBD        Two sides and included angle test.

therefore

angle OAC = angle OBC      corresponding angles in congruent triangles

Now consider AB as the transversal that cuts the lines AC and BD

angle OAC  angle OBC are alternate angles and since they are equal  AC must be parallel to BD

Sep 19, 2018