Q5ii part plz experts answer

Q5ii part plz experts answer c 5. Th figure, given below, shows a trapezium dCD. M and N are the mid-points of the non- parallel sides AD and BC respectively. Find : c 1. In triangle ABC, M is mid-point of AB and a straight line thmugh M and parallel to BC cuts AC at N. Find the lengths of AN and MN, if BC 7 cm and = 5 cm. 2. Prove that the figure obtained by joining the mid-points of the adjacent sides of a rectangle is a rhombus. 3. D, E and F are the mid-points of the sides AB, BC and CA of an isosceles A ABC in which AB = BC. Prove that A DEF is also isosceles. 4. The following figure shows a trapezium ABCD in which AB // DC. P is the mid-point of AD and PR // AB. Prove that : (ii) PR = — DB 6. 8. 9. AB, if DC 20 cm and MN = 27 cm. (iii) DC, if MN = 15 cm and AB = 23 cm. The diagonals of a quadrilateral intersect at I right angles. Prove that the figure obtained by joining the mid-points of the adjacent sides the quadrilateral is a rectangle. 7. L and M are the mid-points of sides AB and DC respectively of parallelogram ABCD Prove that segments DL and BM trise diagonal AC. ABCD is a quadrilateral in which AD BO E, F, G and H are the mid-points of AB, BD CD and AC respectively. Prove that EFGH is a rhombus. PR - — (AB + CD) 2 c A parallelogram ABCD has P the mid-point of DC and Q a point of AC such that AC. PQ produced meets BC at R. 4 Prove that (i) R is the mid-point of BC, 2 (i) MN, if AB = 11 cm and DC = 8 cm. 150