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ICSE Class IX Question Bank 2025 : Mathematics

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CLASS TEST TOPIC MID POINT THEOREM CLASS IX TOTAL MARKS - 22 ........................... LEVEL 1 A. Write proper steps and solve/prove the following: 1) M and N are mid-points of AB and AC. (i) Find x if MNC = (3x 10) and C = (x + 10) (ii) Find y, if MN = (2y + 3) cm and BC = (3y + 8) cm 2) In the quadrilateral ABCD, AD BC. P and Q are mid-points of AB and AC. Prove that (i) R is the mid-point of DC. (ii) AD + BC = 2PR 3) Given is a triangle PQR. X is the mid-point of PQ, Y is the mid-point of QR, and Z is the mid-point of RP. If PQ = 5 cm; QR = 6 cm and PR = 7 cm; then find the length of XY. LEVEL 2 B. Name the Theorem or Property of Triangle you will use in each of the following cases and write the final solution: 1) In the following figure, x, y and z are lines parallel to each other and G is mid-point of CD. Calculate (i) BG if AD = 6 cm (ii) AB if BC = 2.4 cm 2) If D, E and F are mid-points of the sides AB, BC, and CA respectively of an isosceles triangle, prove that DEF is also isosceles. 3) In the adjoining figure, ABCD is a parallelogram and E is mid-point of AD. DL EB meets AB produced at F. Prove that B is mid-point of AF and EB = LF. .. LEVEL 3 1) Street 1 and Street 2 meet at point P, where they are perpendicular to each other. The length of Street 1 is 8 km and Street 2 is 6 km. Car A starts from the end of Street 1 (A), travels straight to reach the end of Street 2 (B) in 10 minutes. Car X starts from the middle point of Street 1 (X) and travels parallel to Car A, to reach Street 2 at position (Y). If the speed of Car X is the same as Car A, then find the time taken by Car X to reach Y.

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