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M.K. MATHEMATICS (M.:8826181724), , CLASS:-IX, , Quadrilateral, , GALACTIC INSTITUTE, MATHEMATICS TEST, TIME: 1.hrs., , [M.M.: 26], , Short Answer Question-I, , (2 marks), , Q.1 In Fig. 14.25, AN and CP are perpendiculars to the diagonal BD of a, parallelogram ABCD. Prove that:, (i) ∆AND ≅ ∆CBP, (ii) AN = CP., , Q.2 In Fig. 14.22, find the four angles A, B, C and D in the parallelogram ABCD., , Q.3 In Fig. 14.49, ABC is an isosceles triangle in which AB = AC. CP || AB and AP is, the bisector of exterior ∠.CAD of ∆ ABC. Prove that (i) ∠PAC = ∠BCA and (ii) ABCP is, a parallelogram., , Q.4 ΔABC is a triangle right angled at B; and P is the mid-point of AC. Prove that, (i) PQ ⊥ AB, (ii) Q is the mid point of AB, Long Answer Question-III, , 60 FEET ROAD, MAHAVIR ENCLAVE PART –III, ABOVE, PUNJAB &SIND BANK, , (3 marks), , Page 1

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M.K. MATHEMATICS (M.:8826181724), , CLASS:-IX, , Quadrilateral, , Q.5 In Fig. 14.75, D, E and F are, respectively the mid-points of sides BC, CA and AB, of an equilateral triangle ABC. Prove that DEF is also an equilateral triangle., , Q.6 Show that the diagonals of a square are equal and bisect each other at right, angles., Long Answer Question-IV, , (4 marks), , Q.7 In Fig. 14.48, ABCD is a parallelogram and X and Y are points on the diagonal BD, such that DX = BY. Prove that, (i) AXCY is a parallelogram, (ii) AX = CY, AY = CX, (iii) ∆AYB ≅ ∆CXD, (iv) ∆AXD ≅ ΔCYB, , Q.8 ABCD is a rhombus and P, Q, R, S are the mid-points of AB, BC, CD, DA, respectively. Prove that PQRS is a rectangle., Q.9 If ΔABC and ADEF are two triangles such that AB, BC are respectively equal and, parallel to DE, EF, then show that, (i) Quadrilateral ABED is a parallelogram, (ii) Quadrilateral BCFE is a parallelogram, (iii) AC = DF, (iv) ΔABC ≅ ∆DEF, , “Education is the movement from darkness to light”, ALL THE BEST, P.BY: MURARI JHA, , 60 FEET ROAD, MAHAVIR ENCLAVE PART –III, ABOVE, PUNJAB &SIND BANK, , Page 2