中线定理

Practice Harder problems from real math contests

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David Altizio
Expii Team

The Midline Theorem in triangle geometry states the following:

Let $\triangle ABC$ be a triangle, and let $D$ and $E$ be the midpoints of line segments $\overline{AB}$ and $\overline{AC}$ respectively. Then $DE=\frac12 BC$ .

In this page I'll walk you through a proof that this is indeed the case before delving into some problems that utilize this.

From the condition, which statements are true?

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The problems run from approachable to very hard, and each is rated by how often real students solve it, so you can pick your next step. These are real problems from the AMC 8, AMC 10, AMC 12 and AIME, the national math competitions for middle and high school students, each with a worked solution on LIVE by Po-Shen Loh.

Midpoint problems 30 from AMC 8, AMC 10, AMC 12, AIME

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中线定理

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