Balbharati solutions for Geometry (Mathematics 2) [English] 9 Standard Maharashtra State Board chapter 2 - Parallel Lines [Latest edition]

In the given figure, line RP || line MS and line DK is their transversal. ∠DHP = 85°.

1. ∠RHD
2. ∠PHG
3. ∠HGS  
4. ∠MGK

In the given figure, line p || line q and line l and line m are transversals. Measures of some angles are shown.

Hence find the measures of, ∠a, ∠b, ∠c, ∠d.

In the given figure, line l || line m and line n || line p.

Find, ∠a, ∠b, ∠c from the given measure of an angle.

In the given figure, sides of ∠PQR and ∠XYZ are parallel to each other.

Prove that, ∠PQR ≅ ∠XYZ.

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. 

1. ∠ART
2. ∠CTQ
3. ∠DTQ
4. ∠PRB

In the given figure, y = 108° and x = 71° Are the lines m and n parallel? Justify.

In the given figure, if ∠a ≅ ∠b then prove that line l || line m.

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

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 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.

A transversal EF of line AB and line CD intersects the lines at point P and Q respectively. Ray PR and ray QS are parallel and bisectors ∠BPQ and ∠PQC respectively. Prove that line AB || line CD.

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

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

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

In ΔABC, ∠A = 76°, ∠B = 48°, ∴ C = ______.

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 ______.

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 -

1. A pair of complementary angles  
2. A pair of supplementary angles. 
3. A pair of congruent angles.

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

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.

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

In the given figure, if line AB || line CF and line BC || line ED then prove that ∠ABC = ∠FDE.

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 `square` QXRY is a rectangle.