Q. 9 The Law of Similar Triangles: Su... [FREE SOLUTION]

Chapter 3: Q. 9 (page 313)

The Law of Similar Triangles: Suppose two right triangles have the same angle measures as each other (i.e., they are similar), where the first has legs of lengths $x_{1}$ and $y_{1}$ and a hypotenuse of length $h_{1}$ and the second has corresponding legs of lengths $x_{2}$ and $y_{2}$ and a hypotenuse of length $h_{2}$ . Then we have the following three equations involving ratios;
, , and __ .

Short Answer

Expert verified

The Law of Similar Triangles: Suppose two right triangles have the same angle measures as each other (i.e., they are similar), where the first has legs of lengths $x_{1}$ and $y_{1}$ and a hypotenuse of length $h_{1}$ and the second has corresponding legs of lengths $x_{2}$ and $y_{2}$ and a hypotenuse of length $h_{2}$ . Then we have the following three equations involving ratios;role="math" localid="1648620426842" $\frac{h_{2}}{y_{2}} = \frac{h_{1}}{y_{1}}, \frac{x_{2}}{y_{2}} = \frac{x_{1}}{y_{1}}, a n d \frac{x_{2}}{h_{2}} = \frac{x_{1}}{h_{1}}$ .

Step by step solution

Step 1. Given information

The Law of Similar Triangles: Suppose two right triangles have the same angle measures as each other (i.e., they are similar), where the first has legs of lengths $x_{1}$ and role="math" localid="1648620561590" $y_{1}$ and a hypotenuse of length $h_{1}$ and the second has corresponding legs of lengths $x_{2}$ and $y_{2}$ and a hypotenuse of length $h_{2}$ . Then we have the following three equations involving ratios; ______, ______, and ______ .

Step 2. The Law of Similar Triangles

The Law of Similar Triangles: Suppose two right triangles have the same angle measures as each other (i.e., they are similar), where the first has legs of lengths $x_{1}$ and $y_{1}$ and a hypotenuse of length $h_{1}$ and the second has corresponding legs of lengths $x_{2}$ and $y_{2}$ and a hypotenuse of length $h_{2}$ . Then we have the following three equations involving ratios; $\frac{h_{2}}{y_{2}} = \frac{h_{1}}{y_{1}}, \frac{x_{2}}{y_{2}} = \frac{x_{1}}{y_{1}}, a n d \frac{x_{2}}{h_{2}} = \frac{x_{1}}{h_{1}}$ .