Question

In the given figure, prove whether the following pairs of lines are parallel or not.
a) Is EF parallel to GH?
b) Is AB parallel to CD?

Answer 1

Step-by-step explanation:

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Answer 2

Given:

Lines AB, CD, EF, and GH arranged as shown in the figure

To find:

a) If EF is parallel to GH

b) If AB is parallel to CD

Solution:

a) ∠NOD = 70°   -- (1)

∠CPF = ∠MPO = 65° (vertically opposite angles are equal)  -- (2)

If EF ║ GH then CD acts as transversal. In this case, ∠NOD and ∠MPO act as corresponding angles which according to the theorem should be equal.

From equations 1 and 2 we can conclude that ∠NOD ≠ ∠MPO

Hence,  EF ∦ GH

b) ∠CPF = ∠MPO = 65° (vertically opposite angles are equal)

If AB ║ CD then EF acts as transversal. In this case, ∠NMP and ∠MPO are interior angles on the same side of transversal hence they should be supplementary.

⇒  ∠MPO + ∠NMP = 65 + 115 = 180°

The sum is 180°

Hence proved that AB ║ CD.