Question

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Please ansr this..

# If a line divides any two sides of a triangle in the same ratio, then the line is parallel to the third side.

Please explain it properly so that I could understand. Then I will mark u brainly!!
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Answer 1

$\mathfrak{The\:Answer\:is}$


If a line divides a line into same ratio, then the line is perpendicular on that line.

Hence, the two angles of that line are 90°(θ = let)

If we take a line (3rd side) next to the perpendicular line,
One of it's angle = 90° (corresponding angles)

We know,

Slope of a line

= tan θ 

= tan 90°

= not defined


As the slope of both the lines are not defined, then they are equal and parallel.

Hence, proved.


$\boxed{Hope\:This\:Helps}$

Answer 2

Step-by-step explanation:

From figure:

Consider a line DE such that (AD/DB) = (AE/EC).

Draw a line DE' parallel to BC(If DE is not parallel to BC).

⇒ (AD/DB) = AE'/E'C     ----------- (1)

In ΔABC,

⇒ (AD/DB) = AE/EC     ---------- (2)

From (1) & (2), we get

⇒ (AE/EC) = AE'/E'C

⇒ (AE/EC) + 1 = (AE'/E'C) + 1

⇒ (AE + EC)/EC = (AE' + E'C)/E'C

⇒ AE/EC = AC/E'C

⇒ EC = E'C

∴ DE ║ BC.

Therefore,