Question

If the given figure e is the mid point of xy and ef I|yz if xz 7cm then find xf

Answer 1

Given:

If the given figure, E is the midpoint of XY and EF I| YZ. if XZ = 7cm then find XF

To find:

XF

Solution:

We know,

$\boxed{\bold{\underline{Converse\:Midpoint\:Theorem}}} :$

This theorem states that if a line is drawn through the midpoint of one side of a triangle and is parallel to its second side, then it will bisect the third side of the triangle.

Here we have,

E is the midpoint of side XY

Also, EF is parallel to YZ

XZ = 7 cm

Now, based on the Converse of Midpoint theorem, we get

EF bisects side XZ

i.e., $XF = \frac{1}{2} \times XZ$

$\implies XF = \frac{1}{2} \times 7$

$\implies \bold{XF = 3.5\:cm}$

Thus, the length of XF is → 3.5 cm.

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Also View:

in a triangle ABC, D is the midpoint of side BC. If a line is drawn from B in such a way that bisects AD and cut AD and AC at E and X respectively, then prove that EX/BE=1/3

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State and explain converse of The midpoint theorem.

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