In Fig. 5.64, find out which pair of lines are parallel
Solution:
Given, the figure represents the lines EF, GH, KP cut by the lines AB and CD.
We have to determine which lines are parallel.
Linear pairs of angles are formed when two lines intersect each other at a single point.
Linear pair angles are supplementary angles as their sum is 180°.
Considering lines EF cut by the line CD,
∠1 + 123° = 180°
∠1 = 180° - 123°
∠1 = 57°
Considering lines GH cut by the line CD,
∠2 + 57° = 180°
∠2 = 180° - 57°
∠2 = 123°
Considering lines EF and GH cut by the line CD,
∠1 + ∠2 = 57° + 123°
= 180°
If two parallel lines are intersected by a transversal, each pair of interior angles on the same side of the transversal is supplementary.
The sum of co interior angles is equal to 180 degrees.
Therefore, the lines EF and GH are parallel.
Considering lines GH cut by the line CD,
∠123° + ∠3 = 180°
∠3 = 180° - 123°
∠3 = 57°
Considering lines KP cut by the line CD,
∠4 + 55° = 180°
∠4 = 180° - 55°
∠4 = 125°
Considering lines EF and GH cut by the line CD,
∠3 + ∠4 = 57° + 125°
= 182°
The sum of co interior angles is not equal to 180 degrees.
Therefore, the lines GH and KP are not parallel.
Considering lines AB and CD cut by the line GH,
∠3 + 122° = 57° + 122°
= 179°
The sum of co interior angles is not equal to 180 degrees.
Therefore, the lines AB and CD are not parallel.
✦ Try This: Which line is parallel to AB?
☛ Also Check: NCERT Solutions for Class 7 Maths Chapter 5
NCERT Exemplar Class 7 Maths Chapter 5 Problem 111
In Fig. 5.64, find out which pair of lines are parallel
Summary:
In Fig. 5.64, the lines EF and GH are parallel.
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