Proportional Parts of Similar Triangles

Let us learn about proportional parts of similar triangles,

Theorem : If two triangles are similar, then the ratio of any two corresponding segments (such as altitudes, medians, or angle bisectors) equals the ratio of any two corresponding sides.

In Figure 1, suppose Δ QRS∼ Δ TUV.

Figure 1 Corresponding segments of similar triangles.

Then,

Then, according to Theorem,

Example 1: Use Figure 2 and the fact that Δ ABC∼ Δ GHI. to find x.

Figure 2 Proportional parts of similar triangles.

Hope the above explanation helped you.

What is Polygon

Let us study about polygon,
A polygon is a flat closed figure made from straight sides. In order to be a polygon, a figure needs to have at least three sides, but it can have more than that. Here are some polygons:

- the triangle, with three sides
- the quadrilateral, with four sides
- the pentagon, with five sides


If the sides are different lengths, then the shape of a polygon will not always be the same. There are many different triangles, for example, that are very different-looking, because their three sides are different from triangle to triangle.

If however the sides of the polygon are all the same length, then the polygon is called regular.

A regular triangle has three equal sides. It is sometimes called an equilateral triangle. It could also be called equiangular, because its three angles are equal too.
A regular quadrilateral has four sides equal and four angles equal. It is also called a square.

But not all polygons are regular.