Question

For any line, if you draw two right triangles using the line as the hypotenuse, do the triangles have to be similar? Why or why not?

Answer 1

Yes .

Let's check your graph

In ∆ADE and ∆ABC

• AD~BC(Parallel to y axis or y axis)
• AE~EC(Passing through origin and same vertice A)
• AB~DE(Translation by 2)

Hence both triangles are similar

Answer 2

• Yes

Explanation:

If the same line holds the hypotenuse of two right triangles, both of the triangles are similar.

This is because they have same ratio of corresponding sides.