if one diagonal of a trapezium divides the other diagonals in the ratio 1:2.prove that one of the parallel side is double the other
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see the figure :
Here ABCD is a trapezium, in which
AB||CD. AC and BD are diagonals , Let both diagonals intersect at O .
for ∆AOB and ∆COD .
AB || CD
so, angle OAB = angle OCD
angle OBD = angle ODC
for A- A similarly rule .
∆AOB ~ ∆COD
so,
AO/OC = OB/OD = AB/DC
but according to question ,
AO/OC =BO/OD = 1/2
so, AB/CD = 1/2
so, CD = 2AB
hence, proved that one of parallel side is double of other.
Here ABCD is a trapezium, in which
AB||CD. AC and BD are diagonals , Let both diagonals intersect at O .
for ∆AOB and ∆COD .
AB || CD
so, angle OAB = angle OCD
angle OBD = angle ODC
for A- A similarly rule .
∆AOB ~ ∆COD
so,
AO/OC = OB/OD = AB/DC
but according to question ,
AO/OC =BO/OD = 1/2
so, AB/CD = 1/2
so, CD = 2AB
hence, proved that one of parallel side is double of other.
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