5-4 Midsegment Theorem Identify the Midsegment of a triangle

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Presentation transcript:

5-4 Midsegment Theorem Identify the Midsegment of a triangle Use the properties of the Midsegement of a triangle A midsegment of a triangle is a segment that connects the midpoints of 2 sides of a triangle. The midsegments and sides of a triangle have a special relationship.

Midsegment Theorem: The segment connecting the midpoints of the two sides of a triangle is parallel to the third side and half as long. B D E A C

Find each of the following. U, V, and W are midpoints. Find each of the following. UW = 6 RT = 16 RW = 8 R U W 8 T V S 12

Using Midpoints to Draw a Triangle You are given midpoints L(4, 2), M(2, 3) N(5, 4). Plot the midpoints in a coordinate plane. Connect these midpoints to form the midsegments. What are the coordinates of the triangle itself? Hint: Find the slopes of the midsegments. The coordinates of the vertices of the triangle are: (1, 1), (3, 5) and _(7, 3)_. Slope of LN is 2, so there is a line parallel to it that has a slope of 2 in which M is the midpoint. N M L