SOLUTION: Given: ABCD is a parallelogram, DE is perpendicular to AB, DF is perpendicular to BC.
Prove: Triangle AED is similar to triangle CFD
Algebra.Com
Question 663949: Given: ABCD is a parallelogram, DE is perpendicular to AB, DF is perpendicular to BC.
Prove: Triangle AED is similar to triangle CFD
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
Angle DCF is congruent to Angle DAB because non-adjacent angles of a parallelogram are congruent. Angle DFC is right by defn perpendicular, as is Angle DEA. DF perpendicular to BC and BC parallel to AD means DF perpendicular to AD, hence Angle ADF is right. The measure of angle ADC is equal to the sum of the measures of angle ADF and angle FDC, hence the measure of angle FDC is equal to the measure of angle ADC minus 90. Similarly (you work out the details) the measure of angle ADE is equal to the measure of angle ADC minus 90. So the measure of angle ADE is equal to the measure of angle FDC. The triangles are similar by AAA. Q.E.D.
John
My calculator said it, I believe it, that settles it
RELATED QUESTIONS
In parallelogram ABCD, AE is perpendicular to BC and AF is perpendicular to CD. Prove... (answered by Edwin McCravy)
given: parallelogram ABCD, line DE is perpendicular to line AC, line BF is perpendicular... (answered by ikleyn)
given ac is = to df
bc is = to ef
prove ab is = to... (answered by Theo)
ABCD is a trapezoid with BC perpendicular to AB and BC perpendicular to CD, AB = 13, BC = (answered by Edwin McCravy)
Given: Quadrilateral ABCD is a parallelogram with diagonals AC and BD intersecting at E.... (answered by fractalier,ikleyn)
Given: ABCD is a Parallelogram, DE is perpendicular to AB, BF is perpendicular to CD.... (answered by tutor_paul)
Complete these proofs
Given: Line DF is congruent to Line EF; Line DF is perpendicular... (answered by solver91311)
Given: Line AB Is Perpendicular To line DE
Prove: Angle ABD Is Congruent To Angle... (answered by solver91311)
given: AB is perpendicular to BC , BC is perpendicular with CD
prove: <7 is congruent... (answered by Alan3354)
