Question
A diagonal of a parallelogram bisects an angle. Will it also bisect the other angle? Give reason.
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Answer
Consider a parallelogram $ABCD$. Given, $\angle1=\angle2$
Since, $ABCD$is a parallelogram $AB\|CD$ and $AC$ is a transversal.
$\therefore\angle1=\angle4\dots(\text{i})$ [alternate angles]
Similarly,$\angle2=\angle3\dots(\text{ii})$ [alternate angles]
But given, $\angle1=\angle2$
$\therefore\angle3=\angle4$ [from Eqs. $(i) \& (ii)$]
Since, $ABCD$is a parallelogram $AB\|CD$ and $AC$ is a transversal.
$\therefore\angle1=\angle4\dots(\text{i})$ [alternate angles]
Similarly,$\angle2=\angle3\dots(\text{ii})$ [alternate angles]
But given, $\angle1=\angle2$
$\therefore\angle3=\angle4$ [from Eqs. $(i) \& (ii)$]
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