Chapter 5.1 Midsegments of Triangles. Vocabularies Midsegment =a segment connecting the midpoints of two sides. In the figure D is the midpoint of and.

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Presentation transcript:

Chapter 5.1 Midsegments of Triangles

Vocabularies Midsegment =a segment connecting the midpoints of two sides. In the figure D is the midpoint of and E is the midpoint of. So, is a midsegment.

Theorem 5.1 Triangle Midsegment Theorem If a segment joins the midpoints of two sides of a triangle, then the segment is parallel to the third side, and is half its length If AD = DB and AE = EC, Then and

Example #1 Find the value of x. Here P is the midpoint of AB, and Q is the midpoint of BC. So, PQ is a midsegment. Therefore by the Triangle Midsegment Theorem, Substitute. The value of x is 3.

Vocabularies Coordinate proof = You proof by using the coordinate. You begin the proof by placing a triangle in a convenient spot on the coordinate plan. You then choose the variables for the coordinates of the vertices

Example #2 In EFG, H, J, and K are midpoints. Find HJ, JK, and FG. HJ= JK= FG=

Example #3 In DEF, A, B, and C are midpoints. Name pairs of parallel segments. Midsegments? Parallel segments? **Hint: There are 3 midsegments, so there should be 3 pairs of parallel segments

Classwork/Homework Take out a piece of paper Pgs #2-32evens, 33