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Using the basic proportionality theorem, prove that a line drawn through the midpoints of one side of a triangle is parallel to the other side that bisects the third side.

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Answered by tanmoyvestige

Answer:

Here is your solution

From the given diagram we get,

The triangle PQR in which S is the midpoint of P and Q such that PS=SQ

A line parallel to QR intersects PR at T such that ST ǁ QR

To prove: T is the midpoint of PR

Proof: S is the midpoint of PQ

Therefore, PS=SQ

=>PS/QS = 1 – – – – – – – (1)

In triangle PQR, ST ǁ QR,

Therefore, PS/SQ = PT / TR [Using the basic proportionality theorem]

=>1 = PT/ TR [from equation (1)]

Therefore, PT = TR

Hence, T is the midpoint of PR

HOPE IT HELPS YOU

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Answered by aastha4865

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Question:-

Using the basic proportionality theorem, prove that a line drawn through the midpoints of one side of a triangle is parallel to the other side that bisects the third side.

Answer:-

Given,ΔABC in which D is the mid point of AB such that,AD=DB

A line parallel to BC intersect AC At E as shown in above figure such that,DE||BC.

To prove E is the mid point of AC

Proof: D is the mid point of AB

Therefore, AD=DB

AD/DB=1____[1]

In Δ ABC,DE||BC

Therefore,AD/DB=AE/EC [by using basic proposnality theorm]

1=AE/EC (From eq 1st)

Therefore,AE=EC

Hence,E is the mid point of AC.

Therefore,proved.

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Students answer this Using the basic proportionality theorem, prove that a line drawn through the midpoints of one side of a triangle is parallel to the other side that bisects the third side.

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Students answer this

Using the basic proportionality theorem, prove that a line drawn through the midpoints of one side of a triangle is parallel to the other side that bisects the third side.