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Question 2: ABCD is a rhombus and P, Q, R and S are the mid-points of the sides AB, BC, CD and DA respectively. Show that the quadrilateral PQRS is a rectangle. Question 1 Question 3
Read MoreQuestion 1: ABCD is a quadrilateral in which P, Q, R and S are mid-points of the sides AB, BC, CD and DA (see Fig 8.29). AC is a diagonal. Show that : (i) SR || AC and SR =…
Read MoreQuestion 12: ABCD is a trapezium in which AB || CD and AD = BC (see Fig. 8.23). Show that (i) ∠A = ∠B (ii) ∠C = ∠D (iii) △ABC ≅ △BAD (iv) diagonal AC = diagonal BD [Hint: Extend…
Read MoreQuestion 11: In △ABC and △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…
Read MoreQuestion 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) △APB ≅ △CQD (ii) AP = CQ Question 9 Question 11
Read MoreQuestion 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) △APD ≅ △CQB (ii) AP = CQ (iii) △AQB ≅ △CPD (iv) AQ =…
Read MoreQuestion 8: ABCD is a rectangle in which diagonal AC bisects ∠A as well as ∠C. Show that: (i) ABCD is a square (ii) diagonal BD bisects ∠B as well as ∠D. Question 7 Question 9
Read MoreQuestion 7: ABCD is a rhombus. Show that diagonal AC bisects ∠A as well as ∠C and diagonal BD bisects ∠B as well as ∠D. Question 6 Question 8
Read MoreQuestion 6: Diagonal AC of a parallelogram ABCD bisects ∠A (see Fig. 8.19). Show that (i) it bisects ∠C also, (ii) ABCD is a rhombus. Question 5 Question 7
Read MoreQuestion 5: Show that if the diagonals of a quadrilateral are equal and bisect each other at right angles, then it is a square. Question 4 Question 6
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