1.

3. Diagonals AC and BD of a trapezium ABCDwith AB II DC intersect each other at thepoint O. Using a similarity criterion for two triangles, show thatOA/OC = OB /OD​

Answer»

Answer:

In △DOC and △BOA,

AB || CD, thus alternate interior ANGLES will be equal,

∠CDO = ∠ABO

Similarly,

∠DCO = ∠BAO

Also, for the two triangles △DOC and △BOA, vertically OPPOSITE angles will be equal;

∠DOC = ∠BOA

Hence, by AAA similarity criterion,

△DOC ~ △BOA

Thus, the corresponding SIDES are proportional.

DO/BO = OC/OA

OA/OC = OB/OD

Hence, proved.


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