Chapter 11.2, Problem 27HP

To determine

To describe: The scale factor of two congruent triangles.

Answer to Problem 27HP

As the ratios of all corresponding sides of two congruent triangles are 1, so it’s required scale factor of two congruent triangles is 1.

Explanation of Solution

Given information: 

Any two congruent triangles, say $\Delta NPQ$ and $\Delta DEF$

Concept used:

The scale factor between two figures is the same ratio of their corresponding sides. And in congruent triangles, the corresponding sides pairs are always equal.

Calculation:

So, in two said congruent triangles $\Delta NPQ$ and$\Delta DEF$ as,

  $NP\cong DE,PQ\cong EF$and$NQ\cong DF$ Corresponding sides), so

Required scale factor of two such triangles $=\frac{NP}{DE}=1=\frac{PQ}{EF}=\frac{NQ}{DF}$

Conclusion: Thus, the scale factor of two congruent triangles is 1 always.