In △abc, m∈ ac and n∈ bc . prove that mn ∥ ab , if: cm/ma= cn/nb

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Step-by-step explanation:

In triangle △ABC, M∈ AC and N∈ BC and

then

and

Consider triangles ABC and MNC. In these triangles,

Hence, by SAS similarity theorem. Similar triangle have congruent corresponding angles, so

Angles ABC and MNC are corresponding angles when lines AB and MN are cut by transversal BC. Since these angles are congruent, by converse of  corresponding angles theorem, lines AB and MN are parallel.

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