# Geometry lesson in plan

## Steiner's Theorem

**Let's have the triangle ABC and the points M, N ∈(BC). If **

**then this relation is true:**

## Proof.

We use small geometric constructions. We build BE || AC, E** **∈AM and CF || AB, F ** **∈ AN.

(angles with parallel sides) (1)

(we know this from the hypothesys) (2)

From (1) and (2) we have,

BE || AC => (acc. Fundamental Theorem of Similarity)

CF || AB => (acc. Fundamental Theorem of Similarity)

From the last two relations we get:

**Keywords: **
plan geometry theorems, theorem Steiner

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