5 4 Theorem The Triangle Midsegment Theorem 5

5 -4 Theorem The. Triangle. Midsegment Theorem 5 -4 The Warm Up Lesson Presentation Lesson Quiz Holt Geometry

5 -4 The Triangle Midsegment Theorem Do Now Holt Geometry

5 -4 The Triangle Midsegment Theorem Objective TSW prove and use properties of triangle midsegments. Holt Geometry

5 -4 The Triangle Midsegment Theorem Vocabulary midsegment of a triangle Holt Geometry

5 -4 The Triangle Midsegment Theorem 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. Holt Geometry

5 -4 The Triangle Midsegment Theorem 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. Step 2 Compare the slopes of MN and XY. Step 3 Compare the heights of MN and XY. Holt Geometry

5 -4 The Triangle Midsegment Theorem Holt Geometry

5 -4 The Triangle Midsegment Theorem 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 Step 1 Find the coordinates of M and N. Holt Geometry

5 -4 The Triangle Midsegment Theorem Holt Geometry

5 -4 The Triangle Midsegment Theorem The relationship shown in Example 1 and 2 is true for the three midsegments of every triangle. Holt Geometry

5 -4 The Triangle Midsegment Theorem Example 3: Using the Triangle Midsegment Theorem Find each measure. BD CA m CBD Holt Geometry

5 -4 The Triangle Midsegment Theorem Example 4 Find each measure. JL MP m MLK Holt Geometry

5 -4 The Triangle Midsegment Theorem Example 5: Indirect Measurement Application 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? Holt Geometry

5 -4 The Triangle Midsegment Theorem Example 6: Indirect Measurement Application Anna wants to find the distance across the base of Capulin Volcano, an extinct volcano in New Mexico. She measures a triangle at one side of the volcano as shown in the diagram. What is AE? Holt Geometry

5 -4 The Triangle Midsegment Theorem Example 7 What if…? Suppose Anna’s result in Example 4 is correct. To check it, she measures a second triangle. How many meters will she measure between H and F? Holt Geometry

5 -4 The Triangle Midsegment Theorem Example 8: Using the Triangle Midsegment Theorem Find each measure. UW m SVU Holt Geometry

5 -4 The Triangle Midsegment Theorem Example 9: Using the Triangle Midsegment Theorem Find the value of n in each triangle. Holt Geometry

5 -4 The Triangle Midsegment Theorem Holt Geometry