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Question

ABCD is a trapezium in which ABCD and AD=BC (see the given figure). Show that ΔABCΔBAD.


Solution


Extend AB such that it intersects CE at point E where CEAD.

Since, ABCD and CEAD, therefore, AECD is a parallelogram.

Since, ABCD is a trapezium, therefore,

ABC+ADC=180

ABC=180θ ...(i)

Also, 

ABC+CBE=180 [Linear Pair]

CBE=θ ...(ii)

Since, AECD is a parallelogram, therefore, BEC=ADC=θ ...(iii)

From (ii) and (iii)

BEC=CBE=θ

Since, AEDC

Therefore, DAE=180θ...(iv) [Angles on same side of transversal are supplementary]

Now, in ΔABC and ΔBAD.

AD=BC [Given]

AB=AB (Common)

DAB=ABC=180θ [From (i) and (iv)]

ΔABCΔBAD by SAS rule.


Mathematics
DUMMY
Standard IX

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