Parallelogram question
- Thread starter lPing7
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The photo has the question and my attempts.
I need to prove LO=OM
For your last line,
PS = QR (opposite sides of parallelogram) => PL = QM,
I think you would need more of a justification to conclude that about those line segments,
such as "When equals are subtracted from equals, the results are equal."
It is given that PO bisects angle P and QO bisects angle Q.
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Without loss of generality we can take the top and bottom of the parallelogram as constant y values and the sides as having a positive slope [other parallelograms are just rotations and shifted versions of this].
So given PO and QO bisect the angles P and Q respectively, consider the slopes of the lines PO, say it is tan(\(\displaystyle \theta)\), what is the slope of the line QO and what is their product? What does that tell you about the angle POQ and, in turn, what does that tell you about the triangles PLO and QMO? From there what does that tell you about the relationship between LO and OM.
EDIT: Actually you don't need that much, just do the alternate interior angles/ exterior angles / 180 degrees in a triangle type of thing.
So given PO and QO bisect the angles P and Q respectively, consider the slopes of the lines PO, say it is tan(\(\displaystyle \theta)\), what is the slope of the line QO and what is their product? What does that tell you about the angle POQ and, in turn, what does that tell you about the triangles PLO and QMO? From there what does that tell you about the relationship between LO and OM.
EDIT: Actually you don't need that much, just do the alternate interior angles/ exterior angles / 180 degrees in a triangle type of thing.
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Yes, my bad. A justification is required