ANSWER
First proved that line p is parallel to line r
to proof
As given in the question
∠1 ≈∠5
∠1 and ∠5 are corresponding angles
by using the property of the corresponding angles
two lines are cut by a transversal so that the corresponding angles are
congruent, then these lines are parallel.
As shown in diagram q is transversal line.
Thus by using the above property
line p is parallel to line r.
proof of 1(a)
REASON
Vertically opposite angle
The pair of angles formed when two lines intersect each other are called vertically opposite angles.
Thus
∠4 and ∠1 are vertically opposite angle
thus
∠4 ≈∠ 1
proof of 2(b)
REASON
Alternate interior angle
the pairs of angles on either side of the transversal and inside the two lines are called the alternate interior angles . If two parallel lines are cut by a transversal, then the alternate interior angles formed are congruent .
as line p is parallel to line r (proof above)
q is transversal
thus
∠4 ≈∠ 5
Hence proved
proof of 3 (c)
As ∠4 ≈∠5 (proof above)
REASON
If two lines are cut by a transversal so that the alternate interior angles
are congruent, then these lines are parallel.
Thus by above property
line p is parallel to line r
Hence proved
