A midsegment of a triangle is a segment that joins the midpoints of two sides of a triangle. Every triangle has exactly 3 midsegments.
Remember that a midpoint is the halfway point. Notice the congruency marks in the diagram. X is the midpoint, therefor XP is congruent to XQ.
Remember that a midpoint is the halfway point. Notice the congruency marks in the diagram. X is the midpoint, therefor XP is congruent to XQ.
A midsegment of a triangle forms several relationships within that triangle. The triangle midsegment theorem, is one of them. This is shown in the diagram. Copy it into your notes.
The midsegment will be half the size of the side it does not touch. So if DE = 10,
BC = 20. If the length of BC were 30, the length of DE would be 15.
The theorem states that the midsegment is parallel to the 3rd side. Note the parallel arrows in the diagram. Since these lines are parallel, the corresponding angles formed will be equal (see the purple congruency marks).
The diagram shows all relationships formed by 1 midsegment of a triangle. In this section you will use these relationships to find missing side lengths and angles of triangles.
The midsegment will be half the size of the side it does not touch. So if DE = 10,
BC = 20. If the length of BC were 30, the length of DE would be 15.
The theorem states that the midsegment is parallel to the 3rd side. Note the parallel arrows in the diagram. Since these lines are parallel, the corresponding angles formed will be equal (see the purple congruency marks).
The diagram shows all relationships formed by 1 midsegment of a triangle. In this section you will use these relationships to find missing side lengths and angles of triangles.
Copy the example below into your notes. Then try the next problem on your own. Select the more help link to see a similar example worked out.
Complete the worksheet posted below.
Now that you have practiced the basics, lets work on setting up equations. Copy the example below into your notes. The try one on your own.
Complete the worksheet posted below.