Triangle Midsegment Calculator
Find midsegments and the medial triangle
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Midsegment Theorem
- • Midsegment is parallel to the third side
- • Midsegment = ½ × (parallel side)
Triangle with Midsegments
Understanding Triangle Midsegments
A midsegment of a triangle is a segment connecting the midpoints of two sides. Every triangle has three midsegments, and together they form the medial triangle.
Midsegment Theorem
A midsegment is:
- Parallel to the third side of the triangle
- Half the length of the third side
The Medial Triangle
The three midsegments form the medial triangle. This triangle has special properties:
- It's similar to the original triangle with scale factor ½
- Its perimeter is half the original triangle's perimeter
- Its area is one-fourth of the original triangle's area
- It divides the original triangle into 4 congruent triangles
Connection to Proportionality
The midsegment theorem is a special case of the Triangle Proportionality Theorem where the dividing line passes through the midpoints (ratio 1:1).
Frequently Asked Questions
What is a midsegment?
A midsegment is a segment connecting the midpoints of two sides of a triangle. Each triangle has three midsegments.
Why is the midsegment half the third side?
By the Triangle Proportionality Theorem, since midpoints divide sides in ratio 1:1, the parallel segment is half the third side.
What is the medial triangle?
The medial triangle is formed by connecting all three midsegments. It's similar to the original with scale factor 1/2.
Why is the medial triangle's area 1/4 of the original?
Since the scale factor is 1/2, the area factor is (1/2)² = 1/4. Also, the original triangle is divided into 4 congruent triangles.
How do midsegments relate to parallel lines?
Each midsegment is parallel to the third side. The three midsegments create a pattern of parallel lines within the triangle.
Are the 4 small triangles congruent?
Yes! The medial triangle and the three corner triangles are all congruent to each other. Each is 1/4 the area of the original.