Question

32. ABCD is parallelogram, diagonals AC and BD
Intersect each other at point M,
Show that: i) A AMB EA CMDii) AM=CM, BM=DM
A
B
M
D
C С​

Answer 1

Answer:

) In a parallelogram ABCD, its diagonals AC and BD intersect each other at point O.

If AC = 12 cm and BD = 9 cm ; find; lengths of OA and OD.

Solution:

When diagonal AC and BD intersect each other at point O,

Then OA=OC=\frac{1}{2}ACOA=OC=

2

1

AC

OB=OD=\frac{1}{2}BDOB=OD=

2

1

BD

OA=\frac{1}{2}\times AC=\frac{1}{2}\times12=6\ cmOA=

2

1

×AC=

2

1

×12=6 cm

OB=\frac{1}{2}\times BD=\frac{1}{2}\times9=4.5\ cmOB=

2

1

×BD=

2

1

×9=4.5 cm