Chapter 6.9, Problem 17HP

To determine

Whether the statement is true or false for:

“If 2 pairs of corresponding sides of 2 triangles are proportional, then you can use indirect measurement to determine the length of a missing side.”

Answer to Problem 17HP

Given statement is TRUE.

Explanation of Solution

Given information: 

The statement,” If two pairs of corresponding sides of two triangles are proportional, then you can use indirect measurement to determine the length of a missing side.”

Concept used:

In similar triangles, the ratios of corresponding sides are equal or in proportion. So, such proportion can be set as:

  $\frac{\text{One side of I triangle}}{\text{Its corresponding side of II triangle}}=\frac{\text{Second side of I triangle}}{\text{Its corresponding side of II triangle}}$

If any three sides of two triangles are given then the fourth missing side can easily be calculated using above proportion, by using cross multiplication method. For, example : If any three sides of two pairs of corresponding sides of two triangles be 5,8 and 12 units, so side corresponding to side 5 units can be calculated indirectly as :

  $\frac{\text{x}}{5}=\frac{8}{12}$

On cross multiply,

  $x=\frac{8\times 5}{12}=\frac{40}{12}=3.33$

Based on above concept and calculation, it is concluded that given statement is TRUE.