ABCD is quadrilateral in which . If , show that and .
Step Drawing the diagram:
ABCD is quadrilateral in which and .
Draw a line through C parallel to DA intersecting AB produced at E.
Step Proving and :
We have, and
(By construction).
Therefore, AECD is a parallelogram.
Therefore, (Opposite sides of a parallelogram)
(Given)
Therefore,
(Angles opposite to equal sides are equal)
Also, (Interior angles on the same side of transversal is supplementary)
And (Linear pair axiom)
[Sum of adjacent angles of parallelogram is supplementary ]
And (Interior angles on the same side of transversal is supplementary)
Hence proved.