5-4 The Triangle midsegment theorem

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Presentation transcript:

5-4 The Triangle midsegment theorem Chapter5 5-4 The Triangle midsegment theorem

objectives Prove and use properties of triangle midsegments.

Midsegment of a triangle A midsegment of a triangle is a segment that joins the midpoints of two sides of the triangle. Every triangle has three midsegments, which form the midsegment triangle.

Example 1: Examining Midsegments in the Coordinate Plane The vertices of ∆XYZ are X(–1, 8), Y(9, 2), and Z(3, –4). M and N are the midpoints of XZ and YZ. Show that and . Step 1 Find the coordinates of M and N.

solution Step 2 Compare the slopes of MN and XY. Since the slopes are the same, they are parallel

solution Step 3 Compare the heights of MN and XY.

Example#2 The vertices of ΔRST are R(–7, 0), S(–3, 6), and T(9, 2). M is the midpoint of RT, and N is the midpoint of ST. Show that and

Midsegment theorem The relationship shown in Example 1 is true for the three midsegments of every triangle.

Example#3 Find each measure. BD Solution: BD = 8.5

Example#4 Find each measure. mCBD mCBD = mBDF mCBD = 26°

Example #5 In an A-frame support, the distance PQ is 46 inches. What is the length of the support ST if S and T are at the midpoints of the sides? ST = 23

Student guided practice Do problems 2-6 in your book page 336

Homework Do problems10-16 in your book page 336