Class 7 Maths
Lines and Angles
Transversal of Parallel lines
The relationships between angles when a pair of parallel line is intersected by a transversal are:
Pairs of corresponding angles are equal.
- ∠2 = ∠6
- ∠1= ∠5
- ∠3 = ∠7
- ∠4 = ∠8
Pairs of alternate interior angles are equal.
- ∠3 =∠6
- ∠4=∠5
Pairs of interior angles on the same side of the transversal are supplementary.
- ∠4 + ∠6 = 180
- ∠3 + ∠5 = 180
Important points:
- When a transversal cuts two lines, such that pairs of corresponding angles are equal, then the lines have to be parallel.
- When a transversal cuts two lines, such that pairs of alternate interior angles are equal, the lines have to be parallel.
- When a transversal cuts two lines, such that pairs of interior angles on the same side of the transversal are supplementary, the lines have to be parallel.
Problem: State the property that is used in each of the following statements?
(i) If a || b, then ∠1 = ∠5.
(ii) If ∠4 = ∠6, then a || b.
(iii) If ∠4 + ∠5 = 180°, then a || b.
Solution:
(i)The property that is being used is that when a pair of parallel lines is intersected by a transversal the pairs of corresponding angles are equal. Lines a and b are parallel.
Angle 1 and 5 are corresponding angles and thus are equal.
(ii) The property that is being used is that when a transversal cuts two lines, such that pairs of alternate interior angles are equal, the lines have to be parallel.
Given, Angle 4 and 6 are alternate interior angles and are equal. Lines a and b are parallel to each other.
(iii) The property that is being used is when a transversal cuts two lines, such that pairs of interior angles on the same side of the transversal are supplementary, the lines have to be parallel.
Angle 4 and 5 are interior angles on the same side of the transversal and are supplementary. Therefore, lines a and b are parallel.
Problem :In the adjoining figure, p || q. Find the unknown angles.
Solution:
Using the property that when a pair of parallel lines is intersected by a transversal the pairs of corresponding angles are equal. Lines p and q are parallel.
Angle d and 125 degrees are corresponding angles. Therefore, d= 125 degrees.
Now, angle d and angle b are vertically opposite angles as they are formed by the intersection of two lines and are opposite to each other.
Therefore, b = d= 125 degrees.
Angle a and b form a linear pair. So, a and b will be supplementary angles.
a + b = 180
a + 125 = 180
a = 55 degrees.
Angle a and c are vertically opposite angles as they are formed by the intersection of two lines and are opposite to each other.
c = a= 55 degrees.
Angle f and 125 degrees form a linear pair. So, f and 125 will be supplementary angles.
f + 125 =180
f =55 degrees.
Angle e and f are vertically opposite angles as they are formed by the intersection of two lines and are opposite to each other.
e = f= 55 degrees.
Problem :In the given figure, the arms of two angles are parallel.
If∠ABC = 70º, then find (i) ∠DGC (ii) ∠DEF
Solution:
The arms of two angles are parallel. So, we get
AB is parallel to DE
BC is parallel to EF
AB is parallel to DE. BC is a transversal. Using the property that when a pair of parallel lines is intersected by a transversal the pairs of corresponding angles are equal.
∠ABC = ∠DGC
∠DGC = 70 degrees.
BC is parallel to EF. DE is a transversal. Using the property that when a pair of parallel lines is intersected by a transversal the pairs of corresponding angles are equal.
∠DGC = ∠DEF
∠DEF = 70 degrees.
Therefore, ∠DEF = ∠DGC = 70 degrees
Class 7 Maths Lines and Angles NCERT Chapter 5 Free Notes for Best Revision
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By highlighting the benefits and strategies of effective revision, you can approach your studies more mindfully and achieve better results in your exams. Best of luck bachhon!
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