In a quadrilateral ABCD AB || CD, BC || AD, AC = 20cm, BD = 10cm, AB = 10cm
| January 28, 2021 | education
In a quadrilateral ABCD AB || CD, BC || AD, AC = 20cm, BD = 10cm, AB = 10cm, the diagonals of the quadrilateral intersect at point O. Find the perimeter of triangle COD.
Since the opposite sides of the quadrilateral are pairwise parallel, the quadrilateral AВСD is a parallelogram.
In a parallelogram, the lengths of the opposite sides are equal, then СD = AB = 10 cm.
The diagonals of the parallelogram, at the point of intersection, are divided in half, then OS = AC / 2 = 20/2 = 10 cm, OD = ВD / 2 = 10/2 = 5 cm.
Determine the perimeter of the СOD triangle.
Rsod = OС + СD + OD = 10 + 10 + 5 = 25 cm.
Answer: The perimeter of the SOD triangle is 25 cm.
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