CBSE Guess > Papers > Important Questions > Class X > Maths > Mathematics By :- Noor Nawaz Khan Mathematics (Important Questions) 2 Marks Q. 1. In the given figure, and are similar. The area of is 9 sq. cm and the area of is 16 sq. cm. If BC = 2.1 cm, find the length of EF. [Delhi 1996][Ans. 2.8 cm] A D Q. 2. In the given figure, and are similar, BC = 3 cm, EF = 4 cm and area of = 54 cm2. Determine the area of . [Delhi 1996] [Ans. 96 sq. cm] A D Q. 3. In the given figure, considering triangles BEP and CPD, prove that BP x PD = EP x PC. [Delhi 1996 C] A Q. 4. In the given figure, AC = 4.2 cm, DC = 6 cm, BC = 10. Determine AB. [Ans. 2.8 cm] A Q. 5. is right angled at B. On the side AC point D is taken such that AD = DC and AB = BD. Find the measure of [Delhi 1998] Q. 6. In a , P and Q are points on the sides AB and AC respectively such that PQ is parallel to BC. Prove that medium AD, drawn from A to BC, bisects PQ. [AI 1998 C] Q. 7. PQR is an isosceles right triangle, right angled at R. Prove that PQ2 = 2PR2. [Delhi 1998 C] Q. 8. In the given figure, DE || BC and AD : DB = 5 : 4. [AI 2000] [Ans. 25/81] Q. 9. In figure Show that PT. QR = PR . ST [Foreign 2000] Q. 10. In figure, LM || NQ and LN || PQ. If MP = 1/3 MN, find the ratio of the areas of . [Foreign 2000] [Ans. 9 : 4] Q. 11. ABC is an isosceles triangle right angled at B. Two equilateral are constructed with side BC and AC as shown in figure. Prove that area of Area of ACE. [Delhi 2001] Q. 12. If AD is the bisector of If AB = 10 cm, AC = 6 cm and BC = 12 cm, find BD and DC. [Delhi 2001] [Ans. 7.5 cm, 4.5 cm] Q. 13. The areas of two similar triangles are 81 cm2 and 49 cm2 respectively. If the altitude of the first triangle is 6.3 cm, find the corresponding altitude of the other [AI 2001] [Ans.8.8 cm] Q. 14. L and M are the mid-points of AB and BC respectively of right-angled at B. Prove that 4LC2 = AB2 + 4BC2. [AI 2001] Q. 15. 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. [AI 2001] [Ans. 3.5 cm] Q. 16. The areas of two similar triangles are 100 cm2 and 49 cm2 respectively. If the altitude of the bigger triangles is 5 cm, find the corresponding altitude of the other. [Delhi 2002] Q. 17. In an equilateral triangle ABC, AD is the altitude drawn from A on side BC. Prove that 3AB2 = 4AD2 [Delhi 2002] A Q. 18. Any point O, inside is joined to its vertices. From a point D on AO, DE is drawn so that DE || AB and EF || BC as shown in figure. Prove that DF || AC. [AI 2000] A Q. 19. If fig., AB || DE and BD || EF. Prove that DC2 = CF x AC. Q. 20. The areas of two similar triangle are 81 cm2 and 49 cm2 respectively. If the altitude of the bigger triangle is 4.5 cm, find the corresponding altitude of the similar triangle. [AI 2002] [Ans. 3.5 cm] 3 Marks Q. 1. P and Q are points on the sides CA and CB respectively of a right-angled at C. Prove that AQ2 + BP2 = AB2 + PQ2. [Delhi 1996] Q. 2. In , if AD is the median, show that AB2 + AC2 = 2[AD2 + BD2]. [Delhi 1998] Q. 3. In the given figure, M is the mid-point of the side CD of parallelogram ABCD. BM, when joined meet AC in L and AD produced in E. Prove that EL = 2BL. [Al 1998; Delhi 1999] A B Q. 4. ABC is a right triangle, right-angled at C. If p is the length of the perpendicular from C to AB and a, b, c have the usual meaning, then prove that [AI 1998] (i) pc = ab (ii) 1/p2 = 1/a2 + 1/b2 Q. 5. In an equilateral triangle PQR, the side QR is trisected at S. Prove that 9PS2 = 7PQ2. [Al 1998] Q. 6. If the diagonals of a quadrilateral divide each other proportionally, prove that it is trapezium. [Foreign 1999] Q. 7. In an isosceles triangle ABC with AB = AC, BD is a perpendicular from B to the side AC. Prove that BD2 – CD2 = 2CD . AD. [Foreign 1999] Q. 8. In figure
5 Marks Q. 1. In a right triangle ABC, right-angled at C, P and Q are points on the sides CA and CB respectively which divide these sides in the ratio 1 : 2. Prove that Q. 2. The ratio of the areas of similar triangles is equal to the ratio of the squares on the corresponding sides, prove. Q. 3. If a line is drawn parallel to one side of a triangle the other two sides are divided in the same ratio, prove. Use this result to prove the following: Q. 4. In a right triangle, prove that the square on the hypotenuse is equal to the sum of the square on the other two sides. Using above, solve the following : Q. 5. In a right-angled triangle, prove that the square on the hypotenuse is equal to the sum of the square on the other two sides. Q. 6. In a right-angled triangle, the square of hypotenuse is equal to the sum of square on other two sides. Prove it. Q. 7. In a triangle, if the square on one side is equal to the sum of the squares on the other two sides, prove that the angle opposite the first side is a right angle. Q. 8. Prove that areas of two similar triangles are in proportion to the squares of their corresponding sides. Use the above theorem and prove the following: Q. 9. Prove that the ratio of the areas of two similar triangle is equal to the ratio of the squares of their corresponding sides. Using the above, do the following: Q. 10. Prove that in a right-angled triangle, the square on the hypotenuse is equal to the sum of the square on the other two sides. Using the above, prove that following: In Prove that AB2 + CD2 = BD2 + AC2. [AI 2004] Q. 11. In a right triangle, prove that the square on the hypotenuse is equal to sum of the square on the other two sides. Using the above result, prove the following: Q. 12. If a line is drawn parallel to one side of a triangle, prove that the other two sides are divided in the same ratio. |
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