How to approach similar triangles problems?

Question

How to solve similar triangle problems? I have no idea how to identify corresponding pairs and make proportions.

Answer 1

Since $\Delta LWY\sim\Delta LYA,$ we obtain $$\frac{LW}{LY}=\frac{LY}{LA}$$ or $$\frac{LW}{\sqrt{3.5^2+7.0^2}}=\frac{\sqrt{3.5^2+7.0^2}}{3.5}$$ or $$LW=17.5.$$

Answer 2

Note that $\Delta LWY$ and $\Delta LYA$ are both right triangle and share LY and angle $\angle L$ thus $\Delta LWY\sim\Delta LYA$ and

$$\frac{\text{hypotenuse}}{\text{short side}}=\frac{LY}{AL}=\frac{LW}{LY}$$

Answer 3

we get two equations $$l^2=x^2+7.0^2$$ ($l=YW$) $$l^2+LY^2=(3.5+x)^2$$ and ($$LY=\sqrt{3.5^3+7.0^2}$$)

Answer 4

Two triangles are similar if and only if they have the same angles. The corresponding pairs of sides are made by the sides which are opposite to congruent angles. This is the way to identify pairs of sides which are directly proportional.