Q. 64.2( 43 Votes )
Prove that a line joining the midpoints of any two sides of a triangle is parallel to the third side. (Using converse of basic proportionality theorem)
To prove that a line joining the midpoints of any two sides of a triangle is parallel to the third side.
⇒ now we know the converse of a basic proportionality theorem is if a line divides any two sides of a triangle in the same ratio then the line must be parallel to the third side.
⇒ Let us assume ABC in which D and E are the mid points of AB and Ac respectively such that
⇒ AD = BD and AE = EC.
⇒ To prove that DE || BC
⇒ D is the midpoint of AB
∴ AD = DB
Also, E is the midpoint of AC
∴ AE = EC
From equation (1) and (2) we get
∴ DE || BC by converse of proportionality thereom
Hence, the line joining the mid points of any two sides of a triangle is parallel to three sides.
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In the given figure, AB||CD||EF. given AB = 7.5 cm, DC = ycm, EF = 4.5cm, BC = x cm. Calculate the values of x and y.
In the given figure, ∠ADE = ∠B
i. Show that ΔABC ~ ΔADE
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i. AB2 = BC . BD
ii. AC2 = BC . DC
iii. AD2 = BD . CD
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