Intersecting Lines and Non-intersecting Lines

Draw four pairs of intersecting lines. Check by actual measurements whether vertically opposite angles are equal or not?

If each of the two lines is parallel to a third line, what relation exists between them?

If two straight lines intersect each other then prove that the ray opposite to the bisector of one of the angles so formed bisects the vertically opposite angle.

If two lines intersect each other, prove that vertically opposite angles are equal. Using this result, find the value of $x$ in the given figure.

Prove that the bisectors of pairs of vertically opposite angles are in the same straight line.

Correct: Two lines are parallel if they do not meet.

In the adjacent figure slant line $t$ intersects the two lines $l$ and $m$ at points $P$ and $Q$ respectively. If $\angle 2=\angle 3=90°$ then prove that line $l$ and $m$ are mutually parallel. What will be value of $\angle 1+\angle 3?$

In the adjacent figure $l\parallel m, p\perp m$ and $p\perp n$

(i) Is $m\parallel n ?$ why $?$ 

(ii) Is $l\parallel n?$ why $?$

(iii) Is  $p\perp l ?$ why $?$

In triangle $ABC$, angle $B$ is a right angle, $M$ is the mid-point of the side $AC$ and the perpendicular $ML$ at $AB$ is drawn from $M$. If $MN$ is perpendicular to $BC$, then show that the shape $LMNB$ is a rectangle.

$ABCD$ is a square and $L,M,N$ and $O$ are the midpoints of the sides $AB,BC,CD$ and $DA$ respectively. Measure the angles and sides observe that shape $LMNO$ is also a square.

$ABCD$ is a trapezium in which $AD\Vert$ $\mathrm{BC}$. Line segments $BL$ and $CM$ are perpendicular to the line $AD$. Show that $BL\Vert CM$ , if $BC=BL$ then show that $BCML$ is a square.

In the given figure, $15$ every angle of quadrilateral $ABCD$ is right angle. Prove that $AB\parallel CD$ and $AD\parallel BC$.

Two lines are said to be parallel if they have

Two lines are said to be parallel if they have

Give a definition for each of the following terms. Are there other terms that need to be defined first? What are they and how might you define them?
(i) parallel lines

Match the values in column I with those in column II:

Match the values in column I with those in column II:

If a transversal intersects two lines in such a way that a pair of alternate interior angles are equal, then the two lines are _____

In the given figure, if $\angle 1 = 130°$ and

$\angle 6 = 60°,$ is $\mathrm{AB} \left|\right| \mathrm{CD}$ ?