Question

Fig. 8.50
17. ABCD is a parallelogram. The sides AB, AD
are produced to E, F so that AB = BE and AD =
DF. Prove that the triangles BEC and DCF are
congruent.
(SO)​

Answer 1

Answer:

abcd is a parallelogram. the sides ab and ad are produced to e and f respectively, such that ab=be and ad=df. prove that triangle bec congruent to triangle dcf

Explanation:

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Answer 2

Answer:

∠BAD=∠CDF (Corresponding angles for parallel lines AB and CD)

∠BAD=∠CBE (Corresponding angles for parallel lines AB and CD)

Thus, ∠CDF=∠CBE (I)

We know, AD=BC (ABCD is a parallelogram)

and AD=DF (Given)

Thus, DF=BC (II)

Similarly, BE=CD (III)

Now, In △CDF and △CBE

∠CDF=∠CBE (From I)

FD=BC (From II)

BE=CD (From III)

Thus, △FDC≅△CBE (SAS rule)

△BEC≅△DCF

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