### SIMILARITY TEST

1.       The ratio of areas of two triangles with equal heights is 3:2. The base of the larger triangle is 18 cm. Find the corresponding base of the smaller triangle.
2.       Using the Basic proportionality theorem, prove that the line joining the mid points of any two sides of a triangle is parallel to the third side and half of it.
3.       A vertical pole of a length 6m casts a shadow of 4 m long on the ground. At the same time a tower casts a shadow 28 m long. Find the height of the tower.
4.       D is a point on side BC of ∆ ABC such that ADC = BAC. Show that AC2 = BC X DC.
5.       Triangle ABC has sides of length 5, 6 and 7 units while ∆ PQR has perimeter of 360 units. If ∆ ABC is similar to ∆ PQR then find the sides of ∆ PQR.