1) ABC is an isosceles triangle, right – angled at C. Prove that AB2
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 cm2
and 64 cm2
respectively. If the median of the first triangle is 12.1cm, find the corresponding median of the other.
6) In ABC, AD is perpendicular to BC. Prove that:
7) In a quadrilateral ABCD, given that <A + <D = 90o. Prove that AC2 + BD2 = AD2 + BC2
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
10) Sides of triangles are given below. Determine which of them are right triangles.In case of a right triangle, write the length of its hypotenuse.
(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 2b
. Find each of its altitudes.
12) Triangle ABC is right – angled at B and D is the mid – point of BC.
Prove that: AC2
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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