CD and RS are the medians of triangleABC and trianglePQR respectively. prove that the ratio of the medians is the same as that of the sides, given that the two triangles are similar.
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10th
Maths
Triangles
Introduction to Similar Triangles
In the figure, CD and RS ar...
MATHS
In the figure, CD and RS are respectively the medians of △ABC and △PQR. If △ABC∼△PQR, prove that
(i) △ADC∼△PSR
(ii)
RS
CD
=
PQ
AB
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VIDEO EXPLANATION
ANSWER
Given:
CD is median of ΔABC
RS is median of ΔPQR
ΔABC∼ΔPQR
To prove that:
(i) ΔADC∼ΔPSR
(ii)
RS
CD
=
PQ
AB
Proof:
(i)
AD=
2
AB
as CD is the median
PS=
2
PQ
as RS is the median
ΔABC∼ΔPQR
⟹
PQ
AB
=
PR
AC
2PS
2AD
=
PR
AC
⟹ΔADC∼ΔPSR
Hence proved
(ii)
ΔADC∼ΔPSR
⟹
RS
CD
=
PQ
AB
Hence proved
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