Q1 (a) In the figure (1) given below, D, E and F are mid-points of the sides BC, CA and AB respectively of ABC. If AB = 6 cm, BC = 4.8 cm and CA= 5.6 cm, find the perimeter of (i) the trapezium FBCE (ii) the triangle DEF. (b) In the figure (2) given below, D and E are mid-points of the sides AB and AC respectively. If BC = 5.6 cm and∠B = 72°, compute (i) DE (ii)∠ADE. (c) In the figure (3) given below, D and E are mid-points of AB, BC respectively and DF || BC. Prove that DBEF is a parallelogram. Calculate AC if AF = 2.6 cm.
Q5 In the adjoining figure, ABCD is a quadrilateral in which P, Q, R and S are mid-points of AB, BC, CD and DA respectively. AC is its diagonal. Show that (i) SR || AC and SR =1/2AC (ii) PQ = SR (iii) PQRS is a parallelogram.
Q8 (a) In the figure (1) given below, ABCD is a parallelogram. E and F are mid-points of the sides AB and CO respectively. The straight lines AF and BF meet the straight lines ED and EC in points G and H respectively. Prove that (i) HEB = HCF (ii) GEHF is a parallelogram. (b) In the diagram (2) given below, ABCD is a parallelogram. E is mid-point of CD and P is a point on AC such that PC = 1/4 AC. EP produced meets BC at F. Prove that (i) F is mid-point of BC (ii) 2EF = BD
Q9 ABC is an isosceles triangle with AB = AC. D, E and F are mid-points of the sides BC, AB and AC respectively. Prove that the line segment AD is perpendicular to EF and is bisected by it.
Q11 (a) In the quadrilateral (1) given below, AD = BC, P, Q, R and S are mid-points of AB, BD, CD and AC respectively. Prove that PQRS is a rhombus. (b) In the figure (2) given below, ABCD is a kite in which BC = CD, AB = AD, E, F, G are mid-points of CD, BC and AB respectively. Prove that: (i) ∠EFG = 90 (ii) The line drawn through G and parallel to FE bisects DA
Q12 In the adjoining figure, the lines l, m and n are parallel to each other, and G is mid-point of CD. Calculate: (i) BG if AD = 6 cm (ii) CF if GE = 2.3 cm (iii) AB if BC = 2.4 cm (iv) ED if FD = 4.4 cm.
