SOLUTION: Given: Parallelogram MATH with diagonal MT Prove: Mt bisects angle AmH and angle ATH

SOLUTION: Given: Parallelogram MATH with diagonal MT Prove: Mt bisects angle AmH and angle ATH

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Question 246805: Given: Parallelogram MATH with diagonal MT
Prove: Mt bisects angle AmH and angle ATH
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

The problem as stated cannot be done. You cannot prove something that in general is not true. Now if MATH were actually a rhombus, that is another story altogether.

Here's the proof that your Prove statement is false in general.

Construct two parallelograms that are on top of one another:

and

such that

is significantly greater than

. Construct the diagonals

and

.

Since angle

is congruent to

but the alleged half-angles

and

are clearly of different measures, the two diagonals cannot be bisectors.

John

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