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

1) ABC is an isosceles triangle, right – angled at C. Prove that AB

2) The areas of two similar triangles ABC and PQR are in the ratio 9 : 16. If BC = 4.5 cm, find the length of QR.

3) The foot of a ladder is 6 m away from a wall and its op reaches a window 8 m above the ground. If the ladder is shifted in such a way that its foot is 8 m away from the wall, to what height does its tip reach?

4) Determine whether the triangle having sides (b – 1) cm, 2√b cm and (b + 1) cm is a right angled triangle.

5) The areas of two similar triangles are 121 cm

6) In ABC, AD is perpendicular to BC. Prove that:

a)AB

b) AB

7) In a quadrilateral ABCD, given that <A + <D = 90

8)Prove that a line drawn through the mid- point of one side of a triangle parallel to another side bisects the third side.

9) Prove that the line joining the mid – points of any two sides of a triangle is parallel to the third side

(i) 7 cm, 24 cm, 25 cm

(ii) 3 cm, 4 cm, 5 cm

(iii) 40 cm, 80 cm, 100 cm

(iv) 13 cm, 12 cm, 5 cm

11) DEF is an equilateral triangle of side 2

12) Triangle ABC is right – angled at B and D is the mid – point of BC.

Prove that: AC

13) The sides of a ABC are in the ratio AB : BC : CA = 1 : √2 : 1. Show that ABC is a right triangle, right – angled at A.

14) A vertical pole of length 6 m casts a shadow 4 m long on the ground and at the same time a tower casts a shadow 28 m long. Find the height of the tower

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