Question

segment PD is the median of triangle PQR. point T is the midpoint of segment PD. produced QT intersect PR at M. show that PM
PR
=1
3. hint draw DN and parallel to QM ​

Answer 1

Answer:

Step-by-step explanation:

PD is median so QD = DR (median divides the side opposite to vertex into equal halves)

T is mid-point of PD

⇒ PT = TD

In ΔPDN

T is mid-point and is ∥ to TM (by construction)

⇒TM is mid-point of PN

PM =MN……………….1

Similarly in ΔQMR

QM ∥ DN (construction)

D is mid –point of QR

⇒ MN = NR…………………..2

From 1 and 2

PM = MN = NR

Or PM = 1/3 PR

⇒PM/PR = 1/3 hence proved

Answer 2

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PD is median so QD = DR (median divides the side opposite to vertex into equal halves)

T is mid-point of PD

⇒ PT = TD

In ΔPDN

T is mid-point and is ∥ to TM (by construction)

⇒TM is mid-point of PN

PM =MN……………….1

Similarly in ΔQMR

QM ∥ DN (construction)

D is mid –point of QR

⇒ MN = NR…………………..2

From 1 and 2

PM = MN = NR

Or PM = 1/3 PR

⇒PM=1/3PR

hence proved