Parallel Lines Maths - Parallel Lines

Two parallel lines are intersected by a transversal. If measure of one of the alternate interior angles is 75° then the measure of the other angle is _____.

In ∆ABC, ∠A = 76°, ∠B = 48°, then ∠C = _____.

A transversal intersects two parallel lines. If the measure of one of the angles is 40°, then the measure of its corresponding angle is ______.

The number of angles formed by a transversal of two lines is _____.

If a transversal intersects two parallel lines then the sum of interior angles on the same side of the transversal is ____.

In the given figure, line PS is a transversal of parallel line AB and line CD. If Ray QX, ray QY, ray RX, ray RY are angle bisectors, then prove that □ QXRY is a rectangle.

Given: line AB || line CD
Rays QX, RX, QY, RY are the bisectors of ∠AQR, ∠QRC, ∠BQR and ∠QRD respectively.
To prove: □QXRY is a rectangle.

In the given figure, if line q || line r, line p is their transversal and if a = 80°, find the values of f and g.

Given: line AB || line CF and line BC || line ED
To prove: ∠ABC = ∠FDE

Prove that, if a line is perpendicular to one of the two parallel lines, then it is perpendicular to the other line also.

Given: line AB || line CD and line EF intersects them at P and Q respectively.
line EF ⊥ line AB
To prove: line EF ⊥ line CD

Prove the Theorem : If a pair of corresponding angles formed by a transversal of two lines is congruent then the two lines are parallel.

Prove the Theorem : If a pair of alternate angles formed by a transversal of two lines is congruent then the two lines are parallel.

In the given figure, Line AB || line CD || line EF and line QP is their transversal. If y : z = 3 : 7 then find the measure of ∠x.

In the given figure, measures of some angles are shown. Using the measures find the measures of ∠x and ∠y and hence show that line l || line m.

Prove the Theorem : If a pair of corresponding angles formed by a transversal of two lines is congruent then the two lines are parallel.

Prove the Theorem : If a pair of alternate angles formed by a transversal of two lines is congruent then the two lines are parallel.

In the given figure, if ∠a ≅ ∠b and ∠x ≅ ∠y, then prove that line l | line n.

Given: ∠a ≅ ∠b and ∠x ≅ ∠y
To prove: line l | line n

Prove theTheorem : The sum of measures of all angles of a triangle is 180°.

In the given figure, ray AE || ray BD, ray AF is the bisector of ∠EAB and ray BC is the bisector of ∠ABD. Prove that line AF || line BC.

Given: Ray AE || ray BD, and
ray AF and ray BC are the bisectors of ∠EAB and ∠ABD respectively.
To prove: line AF || line BC

In the given figure, if ray BA || ray DE, ∠C = 50° and ∠D = 100°. Find the measure of ∠ABC.
(Hint: Draw a line passing through point C and parallel to line AB.)

In the given figure, line AB || line CD and line PQ is transversal. Measure of one of the angles is given. Hence find the measures of the following angles.

i. ∠ART
ii. ∠CTQ
iii. ∠DTQ
iv. ∠PRB

Ray PQ and ray PR are perpendicular to each other. Points B and A are in the interior and exterior of ∠QPR respectively. Ray PB and ray PA are perpendicular to each other.
Draw a figure showing all these rays and write –
i. A pair of complementary angles
ii. A pair of supplementary angles
iii. A pair of congruent angles.

prove the following theorem : If two parallel lines are intersected by a transversal, the interior angles on either side of the transversal are supplementary.