Question

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

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" $\frac{h_2}{y_2}=\frac{h_1}{y_1},\frac{x_2}{y_2}=\frac{x_1}{y_1},and\frac{x_2}{h_2}=\frac{x_1}{h_1}$.

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; $\frac{h_2}{y_2}=\frac{h_1}{y_1},\frac{x_2}{y_2}=\frac{x_1}{y_1},and\frac{x_2}{h_2}=\frac{x_1}{h_1}$ .