In convex quadrilateral ABCD diagonals AC and BD intersect at point O, with AO = OC, angle BAO

| May 19, 2021 | education

In convex quadrilateral ABCD diagonals AC and BD intersect at point O, with AO = OC, angle BAO = angle OCD, AD = 11 cm; AB = 7 cm.The perimeter of triangle BOC is 21 cm. 1) Prove that quadrilateral is ABCD-parallelogram    2) Find the perimeter of the COD triangle.

Consider triangles ABO and OCD. These triangles are equal in terms of equality of the side (AO = OC) and two adjacent angles (<BAO = <OCD, and <BOA = <COD, as opposite angles.)

Hence, AB = CD, as sides in equal triangles against equal angles <BOA = <COD. In addition, Sides AB and CD are parallel, since the angles lying internally crosswise are equal (<BAO = <OCD) for lines AB and CD.

Property of a parallelogram: if opposite sides are equal and parallel in a quadrilateral, then this is a parallelogram, which means that ABCD is also a parallelogram.

BO + OC + BC = 21, BC = AD = 11, BO + OC = OD + OC = 21 – 11 = 10

To find the perimeter of the triangle OCD, you need to know the sum of the semi-diagonals ABCD. CD = AB = 7.

Perimeter OCD = CD + (OD + OC) = 7 + 10 = 17 (cm)



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