Question

conserve of midpoint theorem??

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Answer 1

Answer:

According to the diagram:

$\bullet$ ABC is a triangle.

$\bullet$ D is the mid-point of AB.

$\bullet$ From D, a line DE is drawn parallel to BC, intersect AC at E.

To prove that: E is the mid-point of AC

Proof:

$\bullet$ BD is parallel to CF (by the construction)

$\bullet$ DF is parallel to BC (given)

∴ BDFC is a parallelogram.

Now:

$\implies$ BD = CF

Note: Since the opposite sides of the parallelogram are equal.

$\implies$ AD = BD [D is the mid-point of AB]

$\implies$ AD = CF - - - - (1)

In the triangle AED and CEF,

$\implies$ ∠AED = ∠CEF

$\implies$ ∠ADE = ∠EFC

$\implies$ AD = CF [from (1)]

Therefore:

By the AAS congruency triangles are congruent.

Thus, AE = EC

i.e. E is the mid-point of AC.

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Answered by: Niki Swar, Goa❤️

Answer 2

Step-by-step explanation:

Midpoint Theorem works conversely. Like say if you draw a line parallel to a side of a triangle through one side's midpoint, it will automatically. intersect the midpoint of the remaining side.