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5-4. The Triangle Midsegment Theorem. Warm Up. Lesson Presentation. Lesson Quiz. Holt Geometry. Objective. Prove and use properties of triangle midsegments. Vocabulary. midsegment of a triangle.

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5-4

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  1. 5-4 The Triangle Midsegment Theorem Warm Up Lesson Presentation Lesson Quiz Holt Geometry

  2. Objective Prove and use properties of triangle midsegments.

  3. Vocabulary midsegment of a triangle

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

  5. A special relationship exists for the three midsegments of every triangle.

  6. 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 . Example 1: Examining Midsegments in the Coordinate Plane Step 1Find the coordinates of M and N.

  7. Step 2Compare the slopes of MN and XY. Since the slopes are the same, Example 1 Continued

  8. Step 3Compare the lengths of MN and XY. Therefore, Example 1 Continued

  9. Example 2A: Using the Triangle Midsegment Theorem Find each measure. BD ∆ Midsegment Thm. Substitute 17 for AE. BD = 8.5 Simplify.

  10. Example 2B: Using the Triangle Midsegment Theorem Find each measure. mCBD ∆ Midsegment Thm. mCBD = mBDF Alt. Int. s Thm. mCBD = 26° Substitute 26° for mBDF.

  11. Check It Out! Example 2a Find each measure. JL ∆ Midsegment Thm. Substitute 36 for PN and multiply both sides by 2. 2(36) = JL 72 = JL Simplify.

  12. Check It Out! Example 2b Find each measure. PM ∆ Midsegment Thm. Substitute 97 for LK. PM = 48.5 Simplify.

  13. Check It Out! Example 2c Find each measure. mMLK ∆ Midsegment Thm. mMLK = mJMP Similar triangles mMLK = 102° Substitute.

  14. Lesson Quiz: Part I Use the diagram for Items 1–3. Find each measure. 1.ED 2.AB 3. mBFE 10 14 44°

  15. Lesson Quiz: Part II 4. Find the value of n. 5.∆XYZ is the midsegment triangle of∆WUV. What is the perimeter of∆XYZ? 16 11.5

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