Similar Triangles

Subject – Mathematics

Similar Triangles

1. Prove basic proportionality theorem. Prove that the line draws through the mid point of one side of a    triangle parallel to another side bisects the third side.
2. State and prove Pythagoras theorem. If ABC is an equilateral triangle of side 2a. Prove that altitude AD is a√3.
3. If the triangle ABC. DE ll BC and DE : BC = 4 : 5 find the ratio of  area of triangle ADE to  area of trapezium BCED.
4. Prove that the ratio of the areas of two similar triangles is equal to the ratio of the squares of the    corresponding sides. Using the above theorem, prove that the area of    the equilateral triangle described   on the side of a square is half the area of the equilateral triangle described on its diagonal.
5. The perpendicular AD on the base BC of a triangle ABC interests BC internally at D such that BD = 3CD   Prove that  2AB² = 2AC² + BC².
6. Prove that if the areas of two similar triangles are equal, then the triangles are congruent.
7.  Prove that three times the square of any side of an equilateral triangle is equal to four times the square on the altitude.
8. In a isosceles triangle ABC, AC = BC and ABsquare =2 ACsquare, Prove that C is a right angle.
9. The perimeter of two similar triangles are 24cm and 18cm. If one side of the first triangle is 8 cm, what is the corresponding side of the other triangle?
10. The areas of two similar triangles are 121 cm² and 64 cm² respectively. If the median of the first triangle      is 12.1 cm. Find the corresponding median of the other.