Proving similar triangles in rates of change

[impulsebro89]

Hello,
For these type of rates of change questions, why do you not have to prove the triangles are similar? Is it because the amount of soap is already in the shape of the soap dispenser, and thus you can assume they are similar? Thanks

[RuiAce]

In the rates topic, sometimes similar triangles will be obvious.

A classic example (in fact, also your current example) of when it's obvious is when essentially you have a triangle "nested" in the other, i.e. one triangle is "inside" the other. Note that the "bases" of the inverted triangles here are also clearly parallel, so it's automatic that it passes the equiangular test. Of course, this test fails if we lose the condition of the bases being parallel.

[impulsebro89]

Ok cool, so unless they specifically ask you to prove they are similar triangles you can launch straight into the working out? (in the rates of change topic)

[RuiAce]

That, or if the similar triangles actually aren’t obvious at all