Midsegments of Triangles
A midsegment joins midpoints of two sides and is parallel to the third.
About this topic
A midsegment connects the midpoints of two sides of a triangle. The Midsegment Theorem says it is parallel to the third side and exactly half its length. A triangle has three midsegments, and together they split it into four congruent triangles.
The theorem helps find lengths and prove parallelism, and extends to trapezoids, where the midsegment length is the average of the two bases.
Worked example: in triangle ABC, M is the midpoint of AB and N is the midpoint of AC. If BC = 14, then MN = 7 and MN is parallel to BC. If MN = 2x + 1 and BC = 6x − 6, then 2(2x + 1) = 6x − 6, so x = 4 and BC = 18. For a trapezoid with bases 10 and 16, the midsegment is (10 + 16)/2 = 13.
Builders use midsegments when dividing a frame, and they appear in proofs that the midpoints of any quadrilateral form a parallelogram. A frequent mistake is forgetting that the midsegment is half the third side, not equal to it, or measuring against the wrong side. The segment must connect midpoints, not just any two points on the sides. Mark each midpoint with tick marks and identify the side that is parallel to the midsegment.
Key ideas
- Its length is half the third side
- It cuts the triangle into a smaller similar triangle
- Use for coordinate proofs
Quick check
Use cases: where Midsegments of Triangles helps
- Homework: review the key idea behind Midsegments of Triangles before you start a problem set.
- Exam revision: use the quick check to test whether you can recall Midsegments of Triangles without notes.
- Visual learning: play with the interactive lab to see how Midsegments of Triangles changes when you adjust its inputs.
- Teaching a friend: explain Midsegments of Triangles in your own words, then compare your version with the key ideas.
Number and algebra skills are used in science, engineering, budgeting and computing.
Frequently asked questions
What is Midsegments of Triangles?
A midsegment joins midpoints of two sides and is parallel to the third.
What will I learn in Midsegments of Triangles?
Its length is half the third side. It cuts the triangle into a smaller similar triangle. Use for coordinate proofs.
Is Midsegments of Triangles part of Mathematics?
Yes. It is one of 200 Mathematics topics on LearnViz HighSchoolEdu, with 3 key ideas, a live animation and a quick check.
Does the Midsegments of Triangles lab work on a phone or tablet?
Yes. The animation resizes to fit your screen and supports touch, so you can drag, tap and slide with your finger.
How should I study Midsegments of Triangles?
Read the summary and key ideas first, play with the interactive lab to see the idea in motion, then answer the quick check. If you get a question wrong, go back to the key idea it tests.
Do I need an account, and is my progress saved?
No account is needed. Marking a topic as learned is saved in your own browser, so it stays on that device and is not sent to a server.