DEMO
Look around freely · sample student, nothing is saved
Get the app
05
NCERT Solutions · Maths Ch 5
Parallel and Intersecting Lines
20 questions · 3 exercises
Closed
Open all
Ex 5.1
Ex 5.2
Ex 5.3
NCERT answers with full exam-style working, step by step. Tap a question to open its solution.
1
EXERCISE 5.1 · 6 QUESTIONS
Intersecting Lines and Parallel Lines
Q1
Can two straight lines intersect at more than one point?
(2 marks)
Q2
When two lines intersect, four angles a, b, c, d are formed (a and c opposite each other, b and d opposite each other). What patterns do you observe among these angles? Is this always true for any pair of intersecting lines?
(2 marks)
Q3
List all the linear pairs and vertically opposite angles you observe in Fig. 5.3 (two intersecting lines forming angles a, b, c, d in order).
(2 marks)
Q4
Which pairs of lines appear to be parallel in Fig. 5.6?
(2 marks)
Q5
Activity 2: Take a square sheet of paper. (i) How would you describe the opposite edges? (ii) How would you describe the adjacent edges? (iii) Fold the sheet horizontally in half: how many parallel lines do you see, and how does the new line relate to the vertical sides? (iv) After one more fold, how many parallel lines? After another? Is there a pattern? (v) A vertical fold is ___ to the horizontal lines. (vi) Can you find a fold parallel to the diagonal?
(3 marks)
Q6
Take a square sheet, fold it in the middle and unfold it. Fold the edges towards the centre line and unfold them. Fold the top right and bottom left corners onto the creased line to create triangles (Fig. 5.8). Are a, b and c parallel to p, q and r respectively? Why or why not?
(2 marks)
2
8 QUESTIONS
Exercise 5.2
Q7
Draw some lines perpendicular to the lines given on the dot paper (Fig. 5.10).
(2 marks)
Q8
In Fig. 5.11, mark the parallel lines using the arrow notation (single arrow, double arrow, etc.) and mark the angle between perpendicular lines with a square symbol. (a) How did you spot the perpendicular lines? (b) How did you spot the parallel lines?
(2 marks)
Q9
In the dot paper, draw different sets of parallel lines. The line segments can be of different lengths but should have dots as endpoints.
(2 marks)
Q10
Using your sense of how parallel lines look, draw lines parallel to the line segments on the dot paper. (a) Did you find it challenging to draw some of them? (b) Which ones? (c) How did you do it?
(2 marks)
Q11
In Fig. 5.13, which line is parallel to line a: line b or line c? How do you decide this?
(2 marks)
Q12
Is it possible for all the eight angles formed by a transversal across two lines to have different measurements? Why or why not? What about five different angles ∠6, ∠5, ∠4, ∠3 and ∠2?
(2 marks)
Q13
Can you draw a line parallel to l that goes through point A? How will you do it with the tools from your geometry box? Describe your method.
(2 marks)
Q14
Paper folding: A line t is made perpendicular to line l passing through A, and then a line m is made perpendicular to t through A. Why are lines l and m parallel to each other?
(2 marks)
3
6 QUESTIONS
Exercise 5.3
Q15
Find the angles marked a, b, c, d, e, f, g, h, i and j in Fig. 5.30. (Use the angles on parallel lines.)
(5 marks)
Q16
Find the angle represented by a in each part of Fig. 5.31.
(3 marks)
Q17
In Fig. 5.32, what angles do x and y stand for? (i) A vertical line is perpendicular to two parallel lines and a slanted line makes 65° with it. (ii) Two lines cross on the upper parallel line and make 53° and 78° with the lower parallel line.
(3 marks)
Q18
In Fig. 5.33, ∠ABC = 45° and ∠IKJ = 78°. Find ∠GEH, ∠HEF and ∠FED.
(3 marks)
Q19
In Fig. 5.34, AB is parallel to CD and CD is parallel to EF. Also EA is perpendicular to AB. If ∠BEF = 55°, find the values of x and y.
(3 marks)
Q20
What is the measure of angle ∠NOP in Fig. 5.35? (LM ∥ PQ, ∠LMN = 40°, ∠MNO = 96°, ∠OPQ = 52°.) [Hint: Draw lines parallel to LM and PQ through points N and O.]
(2 marks)