SOLUTION: Given: ABCD is a Parallelogram, DE is perpendicular to AB, BF is perpendicular to CD. Prove: DE congruent to BF the parallegram in the bottom of page 252 is the same exact one

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Question 118490This question is from textbook intergrated mathematics
: Given: ABCD is a Parallelogram, DE is perpendicular to AB, BF is perpendicular to CD.
Prove: DE congruent to BF
the parallegram in the bottom of page 252 is the same exact one for this question ... but this question is not from the text book This question is from textbook intergrated mathematics

Answer by tutor_paul(519)   (Show Source): You can put this solution on YOUR website!
If you draw the diagram, you will see that these two perpendicular lines form right triangles AED and BFC inside the parallelogram. You can prove that these 2 triangles are congruent by the AAS theorem:
- Angle BFC is congruent to Angle AED since they are both right angles (given)
- Angle EAC is congruent to Angle BCF since opposite angles of a parallelogram are congruent.
- Line BC is congruent to Line AD since opposite sides of a parallelogram are congruent.
So you have now shown that the 2 triangles are congruent by AAS.
Since the two triangles are congruent, then by definition of congruent triangles, BF is congruent to DE.
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Good Luck,
tutor_paul@yahoo.com
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