RBSE Solutions Class 6 Maths Chapter 8 Basic Geometrical Concepts and Shapes Exercise 8.2

Rajasthan Board RBSE Class 6 Maths Chapter 8 Basic Geometrical Concepts and Shapes Ex 8.2

 

Question 1. Write the names of parallel and intersecting lines in the figures below.
Answer: After looking at the provided figures:
Parallel lines are those that never meet, like (i) line AB and line CD, and (iv) line MN and line ST.
Intersecting lines are those that cross each other at a point, like (ii) line XY and line WZ, and (i) line PQ and line RS. This means lines can be identified by how they interact.
In simple words: Parallel lines run side-by-side without ever touching. Intersecting lines cross paths at some point.

🎯 Exam Tip: Remember that parallel lines have the same distance between them everywhere, while intersecting lines always form angles at their crossing point.

 

Question 2. If five lines of different lengths pass through a point, then what are the lines called?
Answer: When five lines of different lengths all pass through one single point, they are called concurrent lines. This is a special type of intersection where many lines share one common point.
In simple words: Lines that all meet at the same spot are called concurrent lines.

🎯 Exam Tip: The key characteristic of concurrent lines is that they all share a common point of intersection, regardless of their individual lengths or directions.

 

Question 3. Bisect the line segments of the following lengths and write the length of each part.
(i) 8 cm
(ii) 7.6 cm
(iii) 5.8 cm
(iv) 6.4 cm
Answer: To bisect a line segment means to divide it into two equal parts. We use a compass and ruler for this. Here are the bisections for each given length:
(i) For a line segment of 8 cm:
Draw a line segment AB that is 8 cm long. Now, using a compass, open it more than half the length of AB. Place the compass point on A and draw an arc above and below the line. Repeat this from point B, making sure the arcs cross the first ones. Label these crossing points C and D. Draw a line connecting C and D; this line will cut AB at point O. Point O is the midpoint, making OA and OB two equal parts. Each part will measure 4 cm (8 cm / 2).

(ii) For a line segment of 7.6 cm:
Draw line segment AB = 7.6 cm. Using the same compass method as above, draw arcs from A and B to intersect at C and D. Join C and D to get point O on AB. Each part (OA and OB) will measure 3.8 cm (7.6 cm / 2).

(iii) For a line segment of 5.8 cm:
Draw line segment AB = 5.8 cm. Using the compass method, bisect it. The bisector CD will cut AB at O. Each part (OA and OB) will measure 2.9 cm (5.8 cm / 2).

(iv) For a line segment of 6.4 cm:
Draw line segment AB = 6.4 cm. Bisect it using the same compass and ruler method. The bisector CD will cut AB at O. Each part (OA and OB) will measure 3.2 cm (6.4 cm / 2).

In simple words: To split a line segment perfectly in half, use a compass to draw arcs from both ends. Where these arcs cross, draw a line. This new line will cut the first line exactly in the middle.

🎯 Exam Tip: When bisecting a line segment, make sure your compass opening is always more than half the length of the segment to ensure the arcs intersect clearly.

 

Question 5. Draw a line segment MN and mark a point L on it. With a ruler and compass, draw a perpendicular to MN through the point L.
Answer: Here are the steps to draw a perpendicular line through a point L that lies on line segment MN using a compass and ruler:
1. First, draw a straight line segment and label it MN. Mark a point L anywhere on this line.
2. Place the compass point on L. Open the compass to any convenient radius (not too large or too small) and draw an arc that cuts the line segment MN on both sides of L. Label the points where the arc intersects MN as C and D.
3. Now, place the compass point on C. Open the compass to a radius that is more than half the distance between C and D. Draw an arc above the line MN.
4. Keeping the compass opening the same, place the point on D and draw another arc above the line MN. Make sure this arc crosses the previous one. Label the point where these two arcs intersect as Q.
5. Finally, use a ruler to draw a straight line connecting point Q to point L. This line QL will be perpendicular to MN at point L.

In simple words: To draw a straight up-and-down line (perpendicular) from a point on another line, first draw small arcs on both sides of that point. Then, from these new arc points, draw two bigger arcs above the line that cross each other. Connect this crossing point to your original point, and you have your perpendicular line.

🎯 Exam Tip: Always make sure your arcs are drawn carefully and intersect clearly to get an accurate perpendicular line. The final line must form a perfect 90-degree angle.

 

Question 6. Draw a line segment AB. Taking a point R not on the line AB, draw a perpendicular to AB from R.
Answer: Here are the steps to draw a perpendicular line to segment AB from an external point R, using a compass and ruler:
1. Start by drawing a line segment, AB. Mark a point R somewhere above or below the line AB; this point should not be on the line.
2. Place the compass point on R. Open the compass so its pencil tip can reach and cut the line AB at two distinct points. Draw an arc that intersects AB at two places. Label these intersection points as C and D.
3. Now, move the compass point to C. Open the compass to a radius that is more than half the distance between C and D. Draw an arc below the line AB.
4. Keeping the compass opening the same, place the point on D and draw another arc below the line AB. This arc should cross the first arc you just drew. Label the point where these two arcs intersect as Q.
5. Finally, use a ruler to draw a straight line connecting point R to point Q. This line segment, RQ, will be perpendicular to AB. The point where RQ meets AB can be labeled P, so RP is perpendicular to AB.

In simple words: To draw a line straight down from a point not on a line, first swing an arc from the point that cuts the line twice. Then, from these two cutting points, draw new arcs below the line that cross each other. Connect the original point to where these new arcs cross, and that line will be perpendicular to the first line.

🎯 Exam Tip: When drawing a perpendicular from an external point, ensure your initial arc from the external point crosses the line segment at two distinct places for accurate subsequent construction.