*In what follows we shall explain the solution of some problems involving similar triangles.*We will start with those problems that can be solved with the direct application of the above rules, and then we will upgrade our discussion to explain some practical problems which use the similar triangles principle to be solved.

The ratio of the length of two sides of one triangle to the corresponding sides in the other triangle is the same and the angles between these sides are equal i.e.: $\frac=\frac$ and $\angle A_1 = \angle A_2$ or $\frac=\frac$ and $\angle B_1 = \angle B_2$ or $\frac=\frac$ and $\angle C_1 = \angle C_2$ Be careful not to mix similar triangles with identical triangle.

Identical triangles are those having the same corresponding sides’ lengths.

$\frac = \frac = \frac = \frac \Rightarrow 2.8 \times AC = 1.6 \times (5 AC) = 8 1.6 \times AC$ $(2.8 - 1.6) \times AC = 8 \Rightarrow AC = \frac = 6.67$ We can then use the similarity between triangles ΔACB and ΔAFG or between the triangles ΔADE and ΔAFG.

Scroll down the page for more examples and solutions on how to detect similar triangles and how to use similar triangles to solve problems.

Therefore, $\frac = \frac = \frac = \frac \Rightarrow AB = \frac = 24m$ x = AB - 8 = 24 - 8 = 16m Hence, the new post should be placed at a distance of 16m from the existing post.

Since the construction is forming right-angle triangles, we can calculate the travel distance of the product as follows: $AE = \sqrt = \sqrt = 8.54m$ Similarly, $AC = \sqrt = \sqrt = 25.63m$ which is the distance the product is currently travelling to reach the existing level.

2) the lengths of the sides of each triangle (without the need to know the measures of their angles); 3) the lengths of two sides and the measure of one angle of each triangle.

This angle should be the one formed by the two known sides.

If the triangles are not positioned in this manner, you can match the corresponding sides by looking across from the angles which are marked to be congruent (or known to be congruent) in each triangle.

The ratio of the length of one side of one triangle to the corresponding side in the other triangle is the same i.e.: $\frac=\frac=\frac$ 3.

## Comments Similar Triangles Problem Solving

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