GSEB Class 7 Maths Solutions Chapter 10 Practical Geometry Exercise 10.1

Question 1. Draw a line, say AB, take a point C outside it. Through C, draw a line parallel to AB using ruler and compasses only.
Answer:
Steps of construction:
I. Create a line segment AB, and place a point C beyond it.
II. Indicate another point D on AB and connect CD.
III. Using D as the center and a suitable radius, create an arc that crosses AB at E and CD at F.
IV. From C as the center, and with a radius the same as DE, draw an arc intersecting CD at G.
V. Using G as the center and a radius (opening) matching EF, place a point H on the arc you just drew.
VI. Connect CH to create a line called 'm'.
Therefore, 'm' is the desired line passing through C, such that 'm' runs parallel to AB.

Exam Tip: Remember that parallel lines must always maintain the same distance from each other. The construction method used here leverages properties of angles formed by transversals to guarantee this condition.

Question 2. Draw a line I. Draw a perpendicular to I at any point on I. On this perpendicular choose a point X, 4 cm away from I. Through X, draw a line m parallel to I.
Answer:
Steps of construction:
I. Create a line 'l' and place a point A upon it.
II. At point A, build a 90° angle to make AL line perpendicular to 'l'.
III. Place a point X on AL so that the distance AX measures 4 cm.
IV. At X, create a 90° angle to draw a line 'm' that is perpendicular to AL.
Therefore, 'm' is the necessary line passing through X, such that 'm' runs parallel to 'l'.

Exam Tip: Constructing perpendiculars accurately is crucial for drawing parallel lines. Ensure your 90° angles are precise to avoid errors in parallelism.

Question 3. Let I be a line and P be a point not on I. Through P, draw a line m parallel to I. Now join P to any point Q on I. Choose any other point R on m. Through R, draw a line parallel to PQ. Let this meet I at S. What shape do the two sets of parallel lines enclose?
Answer:
Steps of construction:
I. Create a line 'l' and position a point P externally.
II. Construct line 'm' parallel to 'l' through point P.
III. Select a point Q on line 'l' and connect PQ.
IV. Place a point R on line 'm'.
V. From R, draw a line RS parallel to PQ, ensuring it intersects 'l' at point S.
As line 'l' is parallel to 'm', it means RP is parallel to SQ.
Also, PQ is parallel to RS.
Therefore, PQRS forms a parallelogram.

Exam Tip: A parallelogram is defined by having two pairs of parallel sides. When constructing, verify that both pairs of opposite sides are indeed parallel.