Answer the following
1. In a parallelogram ABCD, E and F are the midpoints of AB and CD respectively. Show that the linesegments AF and EC trisect the diagonal BD.
2. Show that the quadrilateral formed by joining the mid-points of the sides of a rectangle is a rhombus.
3. In a ΔABC, D, E and F are mid-points of sides AB, AC and BC respectively. If DE and DF are joined, find the perimeter of BDEF.
4. ABC is a triangle right angled at C. A line through the mid-point M of hypotenuse AB and parallel to BC intersects AC at D. Show that
(i)MD ⊥ AC
(ii) D is mid-point of AC
(iii) MC = MA = 1/2 AB
5. In the adjoining figure QR=RS Find ∠PSR
6. The angles of quadrilateral are in the ratio 3 : 5 : 9 : 13. Find all the angles of the quadrilateral.
7. In the adjoining figure, D, E and F are mid-points of the sides BC, CA and AB of ∆ABC If AB = 4.3cm, BC = 5.6cm and AC = 3.5cm, find the perimeter of ∆DEF
8. AD is a median of ∆ABC and E is the mid-point of AD. BE Produced meets AC in F. Prove that AF= 1/3 AC
9. Show that the bisectors of angles of a parallelogram form a rectangle.
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