- Similar Figures
- |
- Similar Polygons
- |
- Basic Proportionally Theorem (or Thales Theorem)
- |
- Criteria for Similarity of Triangles
- |
- Different Criterion for similarity of the triangles
- |
- Areas of Similar Triangles
- |
- Pythagoras Theorem
- |
- Converse of Pythagoras Theorem

1) P and Q are the mid – point of the sides CA and CB respectively of a ABC, right angled at C. Prove that:

(i) 4AQ

(ii) 4BP

(iii) 4(AQ

2) The areas of two similar triangles are in the ratio of the squares of the corresponding altitude

3) The areas of two similar triangles are in the ratio of the squares of the corresponding median.

4) The areas of two similar triangles are in the ratio of the squares of the corresponding angle bisector segments.

5) If, AD BE and CF are medians of the ABC, then prove that

3 (AB

6) In an equilateral triangle ABC, D is a point on side BC such that BD = 1/3 BC. Prove that 9AD

7) O is a point in the interior of a triangle ABC, OD - BC, OE - AC and OF - AB. Show that:

a) OA

b) AF

9) D, E and F are respectively the mid – points of sides AB, BC and CA of ABC. Find the ratio of the areas of DEF and ABC

10) E is a point on side CB produced of an isosceles triangle ABC with AB = AC. If AD ⊥ BC and EF ⊥ AC,

prove that Δ ABD ~ Δ ECF

11) O is any point inside a rectangle ABCD. Prove that OB

12) ABCD is a rectangle. Points M and N are on BD such that AM - BD and CN - BD. Prove that BM

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- Mathematics (Class 10) by RD Sharma
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- Mathematics Foundation Course for JEE/AIPMT/Olympiad Class : 10 (by mtg)
- Board + PMT/ IIT Foundation for JEE Main / Advanced: Science & Mathematics, Class - 10
- Class Companion - Class 10 Mathematics