In Fig. 5.65, show that AB || CD
Solution:
Given, the figure represents two lines AB and CD cut by the lines EF and GH.
We have to determine if the lines AB and CD are parallel or not.
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°.
From the figure,
∠CIF + ∠FIJ = 180°
∠CIF + 50° = 180°
∠CIF = 180° - 50°
∠CIF = 130°
If two parallel lines are intersected by a transversal, each pair of corresponding angles are equal.
From the figure,
∠CIF = ∠ALI = 130°
We observe that the corresponding angles are equal.
Therefore, the lines AB and CD are parallel.
✦ Try This: In the given figure, two parallel lines are cut by a transversal. Find the value of x.
☛ Also Check: NCERT Solutions for Class 7 Maths Chapter 5
NCERT Exemplar Class 7 Maths Chapter 5 Problem 112 (i)
In Fig. 5.65, show that AB || CD
Summary:
In Fig. 5.65, it is shown that AB || CD
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