NCERT class 9 maths chapter 8 Quadrilaterals
Question 1:The angles of quadrilateral are in the ratio 3 : 5 : 9 : 13. Find all the angles of the quadrilateral.
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Question 2:If the diagonals of a parallelogram are equal, then show that it is a rectangle.
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Question 3:Show that if the diagonals of a quadrilateral bisect each other at right angles, then it is a rhombus.
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Question 4:Show that the diagonals of a square are equal and bisect each other at right angles.
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Question 5:Show that if the diagonals of a quadrilateral are equal and bisect each other at right angles, then it is a square.
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Question 6:Diagonal AC of a parallelogram ABCD bisects Ð A (see Fig. 8.19). Show that (i) it bisects Ð C also, (ii) ABCD is a rhombus.
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Question 7:ABCD is a rhombus. Show that diagonal AC bisects Ð A as well as Ð C and diagonal BD bisects Ð B as well as Ð D.
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Question 8:ABCD is a rectangle in which diagonal AC bisects Ð A as well as Ð C. Show that: (i) ABCD is a square (ii) diagonal BD bisects Ð B as well as Ð D.
EXERCISE 8.11. The angles of quadrilateral are in
Question 9:In parallelogram ABCD, two points P and Q are taken on diagonal BD such that DP = BQ (see Fig. 8.20). Show that: (i) D APD @ D CQB (ii) AP = CQ (iii) D AQB @ D CPD (iv) AQ = CP (v) APCQ is a parallelogram
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Question 10:ABCD is a parallelogram and AP and CQ are perpendiculars from vertices A and C on diagonal BD (see Fig. 8.21). Show that (i) D APB @ D CQD (ii) AP = CQ
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Question 11:In D ABC and D DEF, AB = DE, AB || DE, BC = EF and BC || EF. Vertices A, B and C are joined to vertices D, E and F respectively (see Fig. 8.22). Show that (i) quadrilateral ABED is a parallelogram (ii) quadrilateral BEFC is a parallelogram (iii) AD || CF and AD = CF (iv) quadrilateral ACFD is a parallelogram (v) AC = DF (vi) D ABC @ D DEF.
Question 12:ABCD is a trapezium in which AB || CD and AD = BC (see Fig. 8.23). Show that (i) Ð A = Ð B (ii) Ð C = Ð D (iii) D ABC @ D BAD (iv) diagonal AC = diagonal BD [Hint : Extend AB and draw a line through C parallel to DA intersecting AB produced at E.]