Prove that if a line divides the sides of a triangle that it intersects proportionally, then the line is parallel to the third side.

You must prove the theorem using only constructions that can be completed using a compass and straightedge or other theorems or postulates. You cannot use the technology as a reason to support any of your statements.

Question

Prove that if a line divides the sides of a triangle that it intersects proportionally, then the line is parallel to the third side.

You must prove the theorem using only constructions that can be completed using a compass and straightedge or other theorems or postulates. You cannot use the technology as a reason to support any of your statements.

anonymous · Answer

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anonymous · Answer

I'm confused with what their asking. Can someone help?

anonymous · Answer

Suppose that the triangle ABC is cut by a line MN, M on AB and N on AC
such that
$$
\frac{AM}{AB}=\frac{AN}{AC}

$$
This implies the two triangles ABC and AMN to be similar and hence
Angl AMN= Angle ABC. Since these are two alternate exterior angels with respect to MN and BC cut by the secant AB, this implies that MN is parallel to BC

anonymous · Answer

Thank you. Sorry it took so long to reply.

anonymous · Answer

YW