In the given figure- AD - DB and AE - EC- Then- BC - DE -D- 4- 1

The correct option is B 2:1It is given that, AD = DB i.e., AD = 1/2 AB Also, as AE = EC we have, AE = 1/2 AC By mid point theorem, we know that the line segm ...

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Standard IX

Mathematics

Midpoint Theorem

In the given ...

Question

In the given figure, AD = DB and AE = EC. Then, $B C : D E =$ ___.

1 : 2

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2 : 1

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1 : 4

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4 : 1

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Solution

The correct option is B $2 : 1$
It is given that, AD = DB
i.e., AD = $\frac{1}{2}$ AB

Also, as AE = EC
we have, AE = $\frac{1}{2}$ AC

By mid-point theorem, we know that the line segment connecting the midpoints of two sides of a triangle is parallel to the third side and is congruent to one half of the third side.
i.e., DE || BC and DE = $\frac{1}{2}$ BC
Thus, BC : DE = 2 :1

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In the given figure, AD = DB and AE = EC. Then, BC:DE=___.

In the given figure, AD = DB and AE = EC. Then, $B C : D E =$ ___.