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Sample Paper Triangles
1.  In ΔLMN, ∟L = 50°and ∟N= 60°. If ΔLMN is similar to ΔPQR, then find ∟Q. (AI CBSE 2009)

2.  If areas of two similar triangles are in the ratio 25:64, write the ratio of their corresponding sides. (AI CBSE 2009)

3.  D, E and F are mid points of sides BC, AC and AB respectively of triangle ABC. Find ar(ΔDEF)/ar(ΔABC). ( AI CBSE 2008)

4.  If one diagonal of a trapezium divides the other diagonal in the ratio 1:2. Prove that one of the parallel sides is double the other. (CBSE 2010)

5.  ABC is a right triangle, right angled at A, and D is the mid-point of AB. Prove that BC2 = CD2 + 3BD2. (AI CBSE 2009 C)

6.  If the diagonals of a quadrilateral divide each other proportionally, prove that it is a trapezium. (CBSE 2008)

7.  Triangle ABC is right angled at B and D is the mid-point of BC. Prove that:- AC2 = 4AD2 . 3AB2.(AI CBSE 2008 C)

8.  E is a point on the side AD produced of a parallelogram ABCD and BE intersects CD at F. Show that ΔABC is similar to ΔCFB. (AI CBSE 2008)

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Q 1. Verify whether 2 is a zero of the polynomial x 3  + 4x 2  - 3x - 18 or not? Solution p(x) = x 3  + 4x 2  - 3x - 18 Now, 2 will be a zero of the polynomial if p(2) = 0. We have: p(2) = (2) 3  + 4(2) 2  - 3(2) - 18        = 8 + 16 - 6 - 18        = 24 - 24        = 0 Thus, 2 is a zero of the polynomial x 3  + 4x 2  - 3x - 18. Q 2. Complete the following. (i) A polynomial of degree three is called a …….polynomial. (ii) A polynomial of degree zero is called a …….polynomial. (iii) A polynomial of degree two is called a …….polynomial. (iv) A polynomial of degree one is called a …….polynomial. Solution (i) A polynomial of degree three is called a cubic polynomial.   (ii) A polynomial of degree zero is called a constant polynomial.   (iii) A polynomial of degree two is called a quadratic polynomial.   (iv) A polynomial of degree one is called a linear polynomial. ...
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