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Byju's Answer
Standard VI
Mathematics
Parallel Lines with a Transversal
Line l and m ...
Question

Line l and m are parallel to each other. A transversal intersects them at points A and B.

i) An arc of suitable measure is taken from B cutting ‘l’ at D and transversal at M (as shown in the figure).

ii) Now, with the same radius and A as centre an arc FG is drawn (as shown in the figure).

What is the relation between ∠FAG and ∠MBD?


A
alternate exterior angles
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B
alternate interior angles
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C
corresponding angles
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D
vertically opposite angles
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Solution

The correct option is B alternate interior angles
∠FAG and ∠MBD are alternate interior angles.

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Q.

Line l and m are parallel to each other. A transversal intersects them at points A and B.

i) An arc of suitable measure is taken from B cutting ‘l’ at D and transversal at M (as shown in the figure).

ii) Now, with the same radius and A as centre an arc FG is drawn (as shown in the figure).

What is the relation between ∠FAG and ∠MBD?


Q. (a) Draw a line l. Draw a perpendicular on l at any point. On this perpendicular, choose a point X, 4 cm away from l. Through X, draw a line m parallel to l.

(b) Line l and m are parallel to each other. A transversal intersects them at points A and B.

i) An arc of suitable measure is taken from B cutting ‘l’ at D and transversal at M (as shown in the figure).

ii) Now, with the same radius and A as the centre an arc FG is drawn (as shown in the figure).

What is the relation between the length of arc DM and arc FG?
[4 MARKS]

Q.

Line l and m are parallel to each other. A transversal intersects them at points A and B.

i) An arc of suitable measure is taken from B cutting ‘l’ at D and transversal at M (as shown in the figure).

ii) Now, with the same radius and A as centre an arc FG is drawn (as shown in the figure).

What is the relation between length of arc DM and arc FG?


Q.

Line l and m are parallel to each other. A transversal intersects them at points A and B.

i) An arc of suitable measure is taken from B cutting ‘l’ at D and transversal at M (as shown in the figure).

ii) Now, with the same radius and A as centre an arc FG is drawn (as shown in the figure).

What is the relation between ∠FAG and ∠MBD?


Q. Arrange the steps marked (i) to (v) in CORRECT order while constructing a line parallel to a given line, through a point not on the line using ruler and compasses only.
Step 1. Take a line 'I' and a point 'A' outside 'l'.
Step 2. Take any point B on I and join B to A.
(i) Now with A as centre and the same radius as in previous step, draw an arc EF cutting AB at G.
(ii) With the same opening as in previous step and with G as centre, draw an arc cutting the arc EF at H.
(iii) With B as centre and a convenient radius, draw an arc cutting I at C and BA at D.
(iv) Now, join AH to draw a line 'm'.
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