Geometry Chapter 2 Points Lines Line Segment Ray And Their Concepts
Question 1. Answer the following questions:
1. How many line segments can be drawn through a fixed point?
Solution:
An infinite number of line segments can be drawn through a fixed point.
Simplification Maths Class 6
2. What is the greatest number of points of intersection at which three noncoincident line segments can be intersected?
Solution:
A maximum number of three non-coincident line segments that can be intersected is three.
Read And Learn More WBBSE Solutions For Class 6 Maths
3. How many line segments can be drawn through three non-collinear points?
Solution:
Three line segments can be drawn through three non-collinear fixed points.
4. What is the maximum number of points of intersection at which two noncoincident line segments can be intersected?
Solution:
The maximum number of points of intersection that the given two non-coincident line segments can be intersected is one only.
WBBSE Class 6 Points and Lines Notes
5. How many endpoints are there in line segment \(\overline{\mathbf{A B}}\)? What are they?
Solution:
There are two endpoints of a line segment \(\overline{\mathbf{A B}}\) and they are A and B.
6. How many endpoints are there in the ray \(\overrightarrow{\mathrm{AB}}\)?
Solution:
The ray \(\overrightarrow{\mathrm{AB}}\) has only one endpoint and this is A.
7. Are the rays \(\overrightarrow{\mathrm{AB}}\) and \(\overrightarrow{\mathrm{BA}}\) the same?
Solution:
No, the rays \(\overrightarrow{\mathrm{AB}}\) and \(\overrightarrow{\mathrm{BA}}\) are not the same, they are in opposite directions to each other.
8. Are the line segments \(\overline{\mathbf{A B}}\) and \(\overline{\mathbf{B A}}\) the same? From which point of view are they the same?
Class 6 Math Solutions WBBSE English Medium
Solution:
Yes, the line segments \(\overline{\mathbf{A B}}\) and \(\overline{\mathbf{B A}}\) are the same.
They are the same in respect of length.
9. Which of the three straight lines, line segments, and a ray has a definite length?
Solution:
The line segment has a definite length
10. How many line segments can be drawn through two given fixed points?
Solution:
Only one line segment can be drawn through two given fixed points.
Question 2. Write the name of the points of intersection of the following figures
1.
Solution:
The points of intersection are A, B, C, D, and O.
Short Questions on Points and Lines
2.
Solution:
The points of intersection are P, Q, R, S, and T.
Question 3. Write the names of line segments and rays of each of the following.
1.
Solution:
The line segments are \(\overline{\mathbf{B C}}\) and \(\overline{\mathbf{C D}}\).
The rays are \(\overrightarrow{\mathrm{BA}}\) and \(\overrightarrow{\mathrm{DE}}\).
2.
Solution:
The only one-line segment is \(\overline{\mathbf{A B}}\)
The rays are \(\overrightarrow{\mathrm{AC}}\) and \(\overrightarrow{\mathrm{BD}}\)
Question 4. From the following figure, answer the following questions.
1. What are the points X, Y, and Z called?
Solution :
The points X, Y, and Z are called collinear points.
2. How many line segments can be drawn through X, Y, and Z ? Name the line segments.
Common Questions About Line Segments
Solution:
Three line segments can be drawn through X, Y, and Z.
The names of the line segments are XY, YZ, and XZ.
Question 5. Give the answer from the figure given alongside.
1. Write the names of the points of intersection in the figure.
Solution :
The names of the points of intersection are A, B, C, D, E, F, and O.
2. Write the names of the collinear points.
The collinear points are
A, O, D.
B, O, E.
C, O, F.
A, E, C.
A, F, B.
B, D, C.
3. Write the names of the line segments.
The line segments are \(\overline{\mathbf{A E}}\), \(\overline{\mathbf{C E}}\), \(\overline{\mathbf{A F}}\), \(\overline{\mathbf{B F}}\), \(\overline{\mathbf{A O}}\), \(\overline{\mathbf{O D}}\), \(\overline{\mathbf{B O}}\), \(\overline{\mathbf{O E}}\), \(\overline{\mathbf{O C}}\), \(\overline{\mathbf{F O}}\), \(\overline{\mathbf{A D}}\), \(\overline{\mathbf{B E}}\), \(\overline{\mathbf{C F}}\), \(\overline{\mathbf{A B}}\), \(\overline{\mathbf{B C}}\), \(\overline{\mathbf{A C}}\), \(\overline{\mathbf{B D}}\), \(\overline{\mathbf{D C}}\).
4. Write the names of the line segments which are either concurrent or coincident.
The concurrent line segments are \(\overline{\mathbf{A D}}\), \(\overline{\mathbf{B C}}\), \(\overline{\mathbf{C F}}\)
Simplification Questions For Class 6
Question 6. From the given figure answer the following questions :
1. Name six line segments:
Solution :
The names of the six line segments are \(\overline{\mathbf{P Q}}\), \(\overline{\mathbf{R S}}\), \(\overline{\mathbf{U V}}\),\(\overline{\mathbf{M N}}\), \(\overline{\mathbf{G H}}\), and \(\overline{\mathbf{A B}}\).
2. Write the names of 3 pairs of intersecting straight lines
3 pairs of intersections in each other straight lines are
\(\stackrel{\leftrightarrow}{\mathrm{PQ}}\) and \(\stackrel{\leftrightarrow}{\mathrm{MN}}\)
\(\stackrel{\leftrightarrow}{\mathrm{RS}}\) and \(\stackrel{\leftrightarrow}{\mathrm{MN}}\)
3. Write the names of 3 pairs of parallel straight lines.
3 pairs of parallel straight lines are
\(\stackrel{\leftrightarrow}{\mathrm{PQ}}\) || \(\stackrel{\leftrightarrow}{\mathrm{RS}}\)
\(\stackrel{\leftrightarrow}{\mathrm{RS}}\) || \(\stackrel{\leftrightarrow}{\mathrm{UV}}\)
and \(\stackrel{\leftrightarrow}{\mathrm{PQ}}\) || \(\stackrel{\leftrightarrow}{\mathrm{UV}}\)
Question 7. From the given figure answer the following questions.
1. PQ + QR = ?
Solution :
PQ + QR
= 2 cm + 3 cm
= 5 cm
PQ + QR = 5 cm
Examples of Real-Life Applications of Lines and Segments
2. PR + QS = ?
Solution :
PR + QS
= (PQ + QR) + (QR + RS)
= (2 cm + 3 cm) + (3 cm + 4 cm)
= 5 cm + 7 cm
= 12 cm.
PR + QS = 12 cm.
3. PS – QS =?
Solution :
PS-QS = (PQ + QR + RS)-(QR + RS)
= (2 cm + 3 cm + 4 cm) – (3 cm + 4 cm)
= 9 cm – 7 cm
= 2 cm.
PS – QS = = 2 cm.
4. PS =?
Solution :
PS = PQ + QR +RS
= 2 cm + 3 cm + 4 cm
= 9 cm.
PS =9 cm.