By using Ganita Prakash Class 7 Solutions and Part 1 Chapter 5 Parallel and Intersecting Lines Class 7 Question Answer, students can improve their problem-solving skills.
Class 7 Maths Chapter 5 Parallel and Intersecting Lines Solutions
Ganita Prakash Class 7 Chapter 5 Solutions
Class 7 Maths Ganita Prakash Chapter 5 Solutions Parallel and Intersecting Lines
5.1. Across the Line
Page: 106-107
Question 1.
How many angles do they form?
Answer:
There are four angles formed.
Question 2.
Can two straight lines intersect at more than one point?
Answer:
Two straight lines can never intersect at more than one point.
Question 3.
In Fig., if ∠a is 120°, can you figure out the measurements of ∠b, ∠c and ∠d, without drawing and measuring them?
Solution:
Yes, ∠b = 180° – ∠b (Linear pair)
= 180° – 120°
= 60°
∠c = ∠a (Vertically opposite angles)
= 120°
∠d = ∠b (Vertically opposite angles)
= 60°
Question 4.
Is this always true for any pair of intersecting lines?
Solution:
Yes, it is true for any pair of intersecting lines.
Page: 108
Question 5.
Figure it Out :
List all the linear pairs and vertically opposite angles you observe in Fig. 5.3 :
Solution:
| Linear Pairs | ∠a and ∠b, ∠b and ∠c, ∠c and ∠d, ∠d and ∠a |
| Pairs of Vertically Opposite Angles | ∠a and ∠c, ∠b and ∠d, |
5.2. Perpendicular Lines
Question 6.
Can you draw a pair of intersecting lines such that all four angles are equal? Can you figure out what will be the measure of each angle?
Solution:
Yes.
Here, if we draw two perpendicular lines then the angles formed will be equal.
Each angle measures 90° in this case.
5.4. Parallel and Perpendicular Lines in Paper Folding
Page: 113-114
Question 7.
Figure it Out :
1. Draw some lines perpendicular to the lines given on the dot paper in Fig. 5.10.
Solution:
2. In Fig., mark the parallel lines using the notation given above (single arrow, double arrow etc.). 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?
Solution:
(a) Two lines are intersecting at the corner of a square.
(b) The two lines are forming opposite sides of a square or two lines are forming diagonals.
3. In following the dot paper, draw different sets of parallel lines. The line segments can be of different lengths but should have dots as endpoints.
Solution:
4. Using your sense of how parallel lines look, try to draw lines parallel to the line segments on this dot paper.
(a) Did you find it challenging to draw some of them?
(b) Which ones?
(c) How did you do it?
Solution:
(a) Yes. Some of them were challenging to draw.
(b) Lines parallel to e, f, g and h.
(c) By considering the dots which were simi-larly aligned.
5. In Fig. 5.13, which line is parallel to line a – line b or line c? How do you decide this?
Solution:
Line ‘b’ is parallel to line ‘a’ we can decide it by using a scale and a set square.
5.5. Transversals
Page: 115
Question 8.
Is it possible for all the eight angles to have different measurements? Why, why not?
Solution:
No. It is not for all angles to have different measurements.
Here, there are pairs of vertically opposite angles which are equal.
∠1 = ∠3, ∠2 = ∠4, ∠6 = ∠8, ∠5 = ∠7.
Question 9.
What about five different angles-6, 5, 4, 3 and 2?
Solution:
Among the above angles, ∠4 and ∠3 are not different angles as they are vertically opposite angles.
∠6 and ∠5 are different angles and are forming a linear pair.
Also, ∠4 and ∠3 have the same characteristics.
5.7. Drawing Parallel Lines
Page: 119-120
Question 10.
Figure it Out :
Can you draw a line parallel to 1, that goes through point A? How will you do it with the tools from your geometry box? Describe your method.
Solution:
Yes.
Step 1: Place scale and a set square in such a manner that line ‘ l ‘ aligns with one of the edges of the set square and scale aligns with its second straight edge.
Step 2: Keeping the scale at its position we move the set square upward until it’s edge is aligned with point A.
Now, we draw a line through A.
This line will be parallel to the given line and will also pass through the point A.
Question 11.
Why are lines l and m parallel to each other?
Solution:
Lines ‘ l ‘ and ‘m’ are parallel to each other as line ‘ l ‘ is aligned with the length of the given page. This is true for the line ‘m’ also.
As a result l || m.
5.8 Alternate Angles
Page: 123-125
Question 12.
Figure it Out :
1. Find the angles marked below.
Solution:
a = [48°] b = [52°] c = [81°]
d = [99°] e = [69°] f = [48°]
g = [122°] h = [75°] i = [54°]
j = [97°]
Reasons :
a = 48° (Alternate interior angles)
b = 52° (Alternate interior angles)
c = 81° (Alternate interior angles)
Also,
c = 180° – 99° (Co-interior angles)
= 81°
d = 99° (Alternate interior angles)
Also,
d = 180°-81° (Co-interior angles)
= 99°
e = 69° (Alternate interior angles)
f = 180° – 132° (Co-interior angles)
= 48°
g = 122° (Corresponding angles)
h = 75° (Alternate interior angles)
i = 54° (Alternate interior angles)
j = 97° (Alternate interior angles)
2. Find the angle represented by a.
Solution:
a = 180°-42° (Co-interior angles)
a°+42° = 180°(Co-interior ∠s)
∴, a = 138°
Also, a° = 180° – 75° = [105°]
a°+ 67° = 90° (ASP)
⇒ a° = 90°-67° = [23°]
3. In the figures below, what angles do x and y stand for?
Solution:
x° + 65° = 90°(Corresponding ∠s)
⇒ x° = 90° – 65°= [25°]
y° = 90° + 65°= [155°]
Second figure :
x° + 53° = 78° (Exterior ∠ property)
⇒ x° = 78° – 53°= [25°]
4. In Fig., ∠ABC = 45° and ∠IKJ = 7 8°. Find angles ∠GEH, ∠HEF, ∠FED
Solution:
∠GEH = ∠DEB (Vertically opposite angles)
∠DEB = ∠ABC (Corresponding angles)
∴ ∠DEB = 45°
⇒ ∠GEH = 45°
∠HEF = ∠KEB (Vertically opposite angles)
∠KED = ∠JKI (Alternate interior angles)
⇒ ∠KEB = ∠DEB = ∠JKI
⇒ ∠KEB + 45° = 78°
⇒ ∠KEB = 78°-45° = 33°
So, ∠HEF = ∠KEB = 33°
⇒ ∠FED +∠FEG = 180° (Linear pair)
⇒ ∠FED + (∠HEF +∠GEH) = 180°
⇒ ∠FED + (33°+45°) = 78°
Therefore, ∠GEH = 45°,
∠HEF = 33° and
∠FED = 78°.
5. In Fig., 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.
Solution:
From the given figure,
y° + 55° = 180° (Co-interior angles)
⇒ y° = 180° – 55° = 125°
x° = y° (Corresponding angles)
⇒ x° = 125°
6. What is the measure of angle ∠NOP in Fig.?
Solution:
Given: LM || PQ
To find: The measure of ∠NOP.
Construction: Through N and O, draw lines || to LM and PQ.
Let us name it AB and CD, respectively.
Procedure: ∠LMN =∠BNM
⇒ ∠BNM = 40°
Since, ∠MNO = 96°
and ∠MNO =∠BNM +∠BNO
⇒ 96° = 40°+∠BNO
⇒ ∠BNO = 96°-40° = 56°
∠NOC = ∠BNO (Alternate interior angles)
= 56°
∠POC = ∠OPQ (Alternate interior angles)
⇒ ∠POC = 52°
Now, a°= ∠NOC +∠POC
= 56° + 52°
= 108°