Practice Questions - Similar Triangles

1. In the following figure , DEFG is a square and ∠BAC = 90° .Prove that DE² = BD x EC.

2. In the following figure , D divides AB such that AD : DB = 3 :2. E is a point on BC such that DE || AC. Find the ratio of the areas of a) ΔABC and ΔBDE b) Trapezium ACED and ΔBED

3. In the following figure , DE || BC and AD : DB = 5 : 4 , find area(ΔDEF)/area(ΔCFB) 

4. There is a stair case as shown in the following figure. Measurements of steps are marked in the figure. Find the straight line distance between A and B.

5. A right triangle has hypotenuse of length p cm and one side of length q cm. If p-q = 1, express the length of third side of the right triangle in terms of p. 
6. By using the Pythagoras Theorem , calculate ar(ΔPQR) from the following figure.

7. Equilateral triangles are drawn on the sides of a right angled triangle. Show that the area of the triangle on the hypotenuse is equal to the sum of the areas of triangles on the other two sides. 
8. If two triangles are equiangular , prove that the ratio of the corresponding sides is same as the ratio of the corresponding medians. 
9. If two triangles are equiangular , prove that the ratio of the corresponding sides is same as the ratio of the corresponding angle bisector segments. 
10. If two triangles are equiangular , prove that the ratio of the corresponding sides is same as the ratio of the corresponding altitudes.