In a parallelogram ABCD, diagonals AC and BD intersect at O. If AO + BO = 4cm then AC + BD is equal to:
1. 6cm
2. 8cm
3. 10cm
4. Information is insufficient to calculate
Answers
ANSWER
i think the answer is option 4
Given:
In a parallelogram ABCD, diagonals AC and BD intersect at O. If AO + BO = 4cm then AC + BD is equal to?
To find:
AC + BD is equal to?
Solution:
Concepts:
The properties of a parallelogram are:
- Opposite sides are parallel.
- Opposite sides are congruent.
- Opposite angles are congruent.
- Diagonals bisect each other.
- Diagonals separate the parallelogram into two congruent triangles.
- Adjacent angles add up to 180°
From the above properties of a parallelogram, we can say that in parallelogram ABCD, we have
AO = OC and BO = OD . . . (1)
It is given that,
AO + BO = 4 cm . . . (2)
from (1), we get
⇒ OC + OD = 4 cm . . . (3)
Now, on adding equations (2) and (3), we get
(AO + BO) + (OC + OD) = 4 + 4
⇒ AO + BO + OC + OD = 8
⇒ AO + OC + OB + OD = 8
∵ AC = AO + OC and BD = BO + OD
⇒ AC + BD = 8 cm ← option (2)
Thus, the value of AC + BD is equal to → 8 cm.
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