Question

AC = 36 cm, and BC = 27 cm.Verify that DE || AB

Answer 1

The Solution:

Given the figure:

We are asked to show that DE and AB are parallel.

`\begin{gathered} \text{ To show that DE}\parallel AB,\text{ we ne ed to show that the ratio of two } \\ \text{corresponding sides of the given triangles are similar.} \end{gathered}`

So, by the similarity theorem, we have

`(AC)/(DC)=(BC)/(EC)`
`(36)/(20)=(27)/(15)`
`(9)/(5)=(9)/(5)`

If a segment is parallel to one side of a triangle and intersects the other two sides, then the triangle formed is similar to the original and the segment that divides the two sides it intersects is proportional.

Thus, the two triangles are similar. So, it follows that line DE is parallel to line AB since the ratios of the two corresponding sides are equal.