Q 8. - Calculus

Question

State the law of similar triangles and give an example of a pair of triangles that illustrate this law. 

Step-by-Step Solution

Answer

The law of similar triangles states that if two right triangles have the same three angle measures, so that one is just a scaled-up version of the other, then the ratios of side lengths on one triangle are equal to the ratios of corresponding side lengths on the other. Specifically, with the side lengths shown in the diagram at the right, we have 

$\frac{h}{b}=\frac{H}{B}, \frac{d}{b}=\frac{D}{B\hspace{0.17em}}, \frac{d}{h}=\frac{D}{H}$

Step 1. Definition of law of similar triangles

The law of similar triangles states that if two right triangles have the same three angle measures, so that one is just a scaled-up version of the other, then the ratios of side lengths on one triangle are equal to the ratios of corresponding side lengths on the other. Specifically, with the side lengths shown in the diagram at the right, we have 

$\frac{h}{b}=\frac{H}{B}, \frac{d}{b}=\frac{D}{B}, \frac{d}{h}=\frac{D}{H}$

Step 2. Example with explanation

Let us suppose we have two triangles with first triangle having sides $13, 12$ and $5$ units and second triangle having sides $52, 48$ and $20$ units

Therefore, According to law of similar triangles

$\frac{13}{52}=\frac{12}{48}=\frac{5}{20}$

$\Rightarrow \frac{1}{4}=\frac{1}{4}=\frac{1}{4}$ [Hence proved]