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.

Two triangles are Similar if the only difference is size (and possibly the need to turn or flip one around).

These triangles are all similar: (Equal angles have been marked with the same number of arcs) Some of them have different sizes and some of them have been turned or flipped.

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.

## Problem Solving With Similar Figures

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.

The road map between Steve’s home and his friend’s as well as the distances known to Steve are as shown in the figure below.

Guide Steve to reach his friend’s house using the shortest path.

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.

## Comments Problem Solving With Similar Figures

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