Triangles Test ...

In triangle ABC, AB = AC = 8 cm, BC = 4 cm and P is a point on AC, such that AP = 6 cm, then find the length of BP.

In the figure given below, $$CD \parallel EF \parallel AB$$. If $$AB= 22.5$$ cm, $$EP= 7.5$$ cm, $$PC= 15$$ cm and $$DC=27$$ cm. Calculate $$EF$$.

In the following figure, $$XY$$ is parallel to $$BC$$, $$AX= 9 $$ cm, $$XB= 4.5$$ cm and $$BC =18$$ cm. Find $$\displaystyle \dfrac{AY}{YC}$$

In the following figure, XY is parallel to $$BC,\  AX= 9 cm$$, $$XB= 4.5$$ cm and $$BC =18$$ cm. Find the value of $$XY$$.

For two triangles, if one angle of a triangle is equal to one angle of the other triangle and the sides including these angles are proportional, then the two triangles are similar. This is called ___ similarity.   

In the figure, XY $$\parallel$$ AC and XY divides the triangular region ABC into two equal areas.

In the trapezium ABCD, side AB $$\parallel$$ side DC. Diagonals AC and DB intersect each other at O.

In the figure, $$\triangle ABC$$ is right angled at $$B$$. $$D$$ is any point on $$AB$$. $$\,seg\,DE\,\bot\, side \,AC$$. If $$AD\,=\,6\,cm,\,AB\,=\,12\,cm\,\,AC\,=\,18\,cm$$. Find $$AE$$.

Find BC, if AB = 7.2 cm.