To prove the two triangles are similar using postulate or theorem.

geduiwelh 2021-08-07 Answered
To prove: The two triangles are similar using postulate or theorem.
Given information:
The system triangles:
image

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Expert Answer

Szeteib
Answered 2021-08-08 Author has 5586 answers

Now consider a figure, BNMLC in which two similar triangles are drawn such that they have a side parallel to the corresponding side.
\(\displaystyle\overline{{{B}{N}}}\le\overline{{{L}{C}}}\)
And when a line intersects two parallel lines, the corresponding angles of the intersections will be similar.
Therefore,
\(\displaystyle\angle{B}\stackrel{\sim}{=}\angle{C}\)
\(\displaystyle\angle{N}\stackrel{\sim}{=}\angle{L}\)
Thus, two angles of \(\displaystyle\triangle{B}{N}{M}\) are congruent to two angles of \(\displaystyle\triangle{C}{L}{M}\), therefore, according to the AA Similarity Postulate, the triangles are similar.
Therefore,
\(\displaystyle\triangle{B}{N}{M}\sim\triangle{C}{L}{M}\)
Hence, \(\displaystyle\triangle{B}{N}{M}\ {\quad\text{and}\quad}\ \triangle{C}{L}{M}\) are similar with each other by the AA similarity theorem.

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