Question

In the given figure alongside , $BA\parallel DF,CA\parallel EG\&BD\parallel EC$ .
prove that
i) $BG=DF$
ii) $EG=CF$

Answer 1

Given: $BA\parallel DF,CA\parallel EG,BD=EC$

TO PROVE: 1) $BG=DF$

2) $EG=CF$

PROOF:

STATEMENT AND REASON

IN $\Delta BGE$ AND $\Delta DFC$ ,

1. $\angle GBE=\angle FDC$ REASON CORRESPONDING ANGLES AS $BA\parallel DF$

2. $\angle GEB=\angle FCD$ REASON CORRESPONDING ANGLES AS $CA\parallel EG$

3. $BC=BC$

$\Rightarrow BC-BD=BC-EC$

$\Rightarrow CD=BE$ REASON SINCE $BD=EC$

4. $\Delta BGE\cong \Delta DFC$ REASON ASA CONGRUENCY CRITERION

5. $BG=DF$ REASON C.P.C.T

6. $EG=CF$ C.P.C.T

HENCE, PROVED