SOLUTION: Hello! I need to prove that a quadrilateral ABCD is a trapezoid. We are given that the two upper angles are congruent and the two lower angles are congruent. Our hint is that we

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Question 30714: Hello! I need to prove that a quadrilateral ABCD is a trapezoid. We are given that the two upper angles are congruent and the two lower angles are congruent. Our hint is that we need to use the theorem that the sum of the vertex angles of a quadrilateral is 360 degrees. Help!!!
~Katie
Answer by venugopalramana(3286) About Me  (Show Source):
You can put this solution on YOUR website!
LET ABCD BE THE QUADRILATERAL...WE ARE GIVEN
ANGLE A = ANGLE B = X SAY.....AND
ANGLE C = ANGLE D = Y SAY......
SUM OF 4 ANGLES IN A QUADRILATERAL =360...SO
X+Y+X+Y = 360
2(X+Y)=360
X+Y=180
NOW SINCE AB AND CD ARE 2 LINES AND BC IS A TRANSVERSAL,WE HAVE 2 INTERIOR ANGLES
ON THE SAME SIDE OF TRANSVERSAL..NAMELY ANGLE B =X AND ANGLE C =Y....THEIR SUM
X+Y = 180.....HENCE THEY SHOULD BE PARALLEL.
SO AB IS PARALLEL TO CD...HENCE ABCD IS A TRAPEZOID.