Hi, yazzysyed.
As the picture is drawn, we don't have that angles A and C are congruent. In the posted diagram of the assumed parallelogram the statement should be that angles A and C are supplementary (meaning their sum is 180 degrees).
Here is the figure: http://i1250.photobucket.com/albums/.../Picture11.png
And here is the proof: http://i1250.photobucket.com/albums/.../Picture12.png
Hi, yazzysyed.
As the picture is drawn, we don't have that angles A and C are congruent. In the posted diagram of the assumed parallelogram the statement should be that angles A and C are supplementary (meaning their sum is 180 degrees).
The easiest way is to put the parallelogram inside two sets of parallel lines,
then use "angle in parallel lines" facts (alternate, corresponding and vertically opposite angles are equal, angles in a straight line and cointerior angles add to 180 degrees).
hope this is not too late...
for number 3 reason: "Given two lines cut by a transversal. If a pair of interior angles on same side of the transversal are supplementary, the lines are parallel. Source: Geometry Theorems 9.1-25 flashcards | Quizlet
for number 5 reason: the same in number 3.
for number 6 statement: angle A is congruent to angle D .
for number 7 reason: same in number 3 reason.
for number 8 statement: angle A is congruent to angle C