Given the details above, the sequence of steps below shows that ABCD is a Trapezoid.
What is a Trapezoid?
A trapezoid, also known as a trapezium, is a closed, flat object with four straight sides and one set of parallel sides. A trapezium's parallel sides are known as the bases, while its non-parallel sides are known as the legs.
Given:
The diagonals of the quadrilateral ABCD intersect at o where AO/BO = CO/DO; which also means that
AO/CO = BO/DO the proof is given as follows:
Create line OE || DC in a way that E lies on BC.
In ΔBDC, based on the Basic Proportionality Theory,
BO/OD = BE/EC ............................1
It is also given that:
AO/CO = BO/DO ..........................2
Hence, from Equations 1 and 2,
AO/CO = BE/EC
Thus, we can state that on the basis of the Converse of the Basic Proportionality Theorem,
OE || AB
Since AB || OE || DC, it is correct to state that ABCD is a Trapezoid.
Learn more about Trapezoid:
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