NCERT Solutions for Chapter: Lines and Angles, Exercise 3: Exercise

$AP$ and $BQ$ are the bisectors of the two alternate interior angles formed by intersection of a transversal $t$ with the parallel lines $l$ and $m$. See the given figure. Show that $AP\parallel BQ.$

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If in the given figure, bisectors $AP$ and $BQ$of the alternate interior angles are parallel, then show that $l\parallel m$.

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In the given figure, $BA\parallel ED$ and $BC\parallel EF$. Show that $\angle ABC=\angle DEF.$

[Hint: Produce $DE$ to intersect $BC$at $P$ (say)].

In the given figure, $BA\parallel ED$and$BC\parallel EF$. Show that $\angle ABC+\angle DEF=180°.$

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In the given figure, $DE\parallel QR$ and$AP$and $BP$ are the bisectors of $\angle EAB$and $\angle RBA$, respectively. Find $\angle APB$.

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The angles of a triangle are in the ratio $2 : 3 : 4$. Find the angles of the triangle.

A triangle $ABC$ is right angled at $A. L$ is a point on $BC$ such that $AL\perp BC$. Prove that $\angle BAL=\angle ACB.$

Two lines are respectively perpendicular to two parallel lines. Show that they are parallel to each other.