Midsegment Theorem Math Example 1

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Example 1

easy
In △ABC\triangle ABC, MM is the midpoint of ABAB and NN is the midpoint of ACAC. If BC=18BC = 18, find MNMN.

Solution

  1. 1
    Step 1: Identify that MNMN is the midsegment of △ABC\triangle ABC connecting the midpoints of two sides.
  2. 2
    Step 2: By the Midsegment Theorem, the midsegment is parallel to the third side and equal to half its length.
  3. 3
    Step 3: MN=12×BC=12×18=9MN = \frac{1}{2} \times BC = \frac{1}{2} \times 18 = 9.

Answer

MN=9MN = 9.
The Midsegment Theorem states that the segment connecting the midpoints of two sides of a triangle is parallel to the third side and exactly half as long. This theorem is a special case of similar triangles — the smaller triangle formed is similar to the original with ratio 1:2.

About Midsegment Theorem

A segment connecting the midpoints of two sides of a triangle is parallel to the third side and exactly half its length.

Learn more about Midsegment Theorem →

More Midsegment Theorem Examples

Example 2 medium

In [formula], [formula] is the midpoint of [formula] and [formula] is the midpoint of [formula]. If

Example 3 easy

The midsegment of a triangle has length 14. What is the length of the side parallel to the midsegmen

Example 4 hard

In [formula], the three midsegments are drawn, dividing the triangle into four smaller triangles. If

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