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.