Triangles Test ...

Which Similarity criteria will be used to prove: $$\displaystyle \Delta BCD\sim \Delta BAD$$?

Both triangles are similar by $$SAS$$ similarity rule. Find the ratio by which they are similar. 

If $$\triangle PQR$$ and $$\triangle STU$$ are similar, find value of $$x.$$

In $$\triangle ABC, \angle A = 90^o$$ & $$\angle B = 30^o$$. In $$\triangle DEF, \angle E = 30^o$$ & $$\angle F = 60^o$$.

Determine by choosing the best option for the similarly of triangles theorem. $$DE || BC$$. Both $$\triangle ADE$$ & $$ \triangle ABC$$ are similar by:

$$\displaystyle DE\parallel QR$$, $$D, E, F $$ are midpoints of sides $$PQ, PR$$ and $$QR$$. By which rule are triangles formed equal?

Find the value of $$x$$ when $$DE \parallel AB.$$

Diagonals of trapezium $$ABCD$$ intersect at $$O$$ and $$AB \parallel DC$$.
If $$AB = 3CD$$. Find ratio of areas of $$\triangle AOB $$ & $$\triangle COD$$

Converse of Pythagoras theorem states that in a triangle, if the square of larger side is equal to the sum of the squares of the  other two sides, then the angle opposite the first side is a right angle. What are we proving here? We prove $$\displaystyle \angle B=$$........ .

The triangles   $$\triangle ABC$$ & $$\triangle EBD$$   are similar by $$SAS$$ test. Find $$BD.$$