Question

State true or false:

In the following figure, $ABCD$ is a parallelogram, then

$AP$ bisects angle $A$

• A. True
• B. False

Answer 1

The correct option is A True

$GivenABCDisaparallelogram,AD\parallel BC,AB\parallel DC\&AD=DP=PCSoAD=DP=PC=BCLet\angle DAP=\angle 2\&\angle CBP=\angle 1Inisosceles△ADP,\angle DAP=\angle DPA=\angle 2Inisosceles△PCB,\angle CPB=\angle CBP=\angle 1Construction-DrawPQfromPsuchthatPQ=BC=AD\&PQ\parallel BC\parallel AD.SoADPQ\&BCPQarebothparallelograms.NowDP\parallel AQ\&APisthetransversal.\angle DPA=\angle PAQ=\angle 2\{AlternateangleswhenDP\parallel AQ\&APisthetransversal\}\Rightarrow \angle PAQ=\angle DAP\Rightarrow APistheanglebisectorof\angle A$