Introduction to Similar Triangles

Let us understand what are similar triangles,
In general, to prove that two polygons are similar, you must show that all pairs of corresponding angles are equal and that all ratios of pairs of corresponding sides are equal. In triangles, though, this is not necessary.
Two angles of one triangle are equal to two angles of another triangle, then the triangles are similar.

Example 1: Use Figure 1 to show that the triangles are similar.

Figure 1 Similar triangles.

AA Similarity Postulate, Δ ABC ∼ Δ DEF. Additionally, because the triangles are now similar,

Hope the above explanation helped you.

The Midpoint Theorem

Let us understand what is midpoint theorem,

Figure 1 shows Δ ABC with D and E as midpoints of sides AC and AB respectively. If you look at this triangle as though it were a trapezoid with one base of BC and the other base so small that its length is virtually zero, you could apply the “median” theorem of trapezoids, Theorem 55.


Theorem 56 (Midpoint Theorem): The segment joining the midpoints of two sides of a triangle is parallel to the third side and half as long as the third side.

In Figure 1 , by Theorem 56,


Hope the above explanation helped you, now let me on properties of trapezoids.