maths

BD = CE

State whether the above statement is true or false.

$∠ABC=∠ACB$ (Isosceles triangle property)

$∠DBC=∠ECB$ (Given)

hence, $∠DBC−∠ABC=∠ECB−∠ACB$

Thus, $∠DBA=∠ECA$

In $△ABD$ and $△ACE$

$∠DBA=∠ECA$ (Proved above)

$AB=AC$ (Given)

$∠DAB=∠EAC$ (Vertically opposite angles)

Thus, $△ABD≅△ACE$ (SAS rule)

Hence, $BD=CE$(Corresponding sides)

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$∠CAD=∠BAE$

**State whether the above statement is true or false.**

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i) $AM=AN$

ii) $ΔAMC≅ΔANB$

iii) $BN=CM$

iv) $ΔBMC≅ΔCNB$

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