Question

the two triangles have at least two pairs of congruent corresponding angles, so the two triangles are similar by the angle - angle theorem. thus, the two triangles have the same ratio of height to width. the height - to - width ratio of each triangle is equal to. the height - to - width ratio of each triangle is the of the line.

Explanation:

Step1: Recall ratio formula

The height - to - width ratio is calculated as $\frac{\text{height}}{\text{width}}$.

Step2: Calculate ratio for first triangle

For the first triangle with height 2 and width 1 (assuming a base of 1 for the right - angled triangle), the ratio is $\frac{2}{1}=2$.

Step3: Calculate ratio for second triangle

For the second triangle with height 5 and width 2.5 (since the triangles are similar, the ratio is consistent), the ratio is $\frac{5}{2.5} = 2$.

Answer:

2