5 4 The Triangle Midsegment Theorem Warm UpPass

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5 -4 The Triangle Midsegment Theorem Warm Up(Pass Back Papers) Use the points A(2,

5 -4 The Triangle Midsegment Theorem Warm Up(Pass Back Papers) Use the points A(2, 2), B(12, 2) and C(4, 8) for Exercises 1– 4. 1. Find the midpoints of AC. 2. Find AC. 5 3. Find the slope of AB. 0 4. What is the slope of a line parallel to 3 x + 2 y = 12? Holt Geometry (3, 5)

5 -4 The Triangle Midsegment Theorem Holt Geometry

5 -4 The Triangle Midsegment Theorem Holt Geometry

5 -4 The Triangle Midsegment Theorem A midsegment of a triangle is a segment

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 The vertices of ∆XYZ are X(– 1, 8),

5 -4 The Triangle Midsegment Theorem 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. Holt Geometry

5 -4 The Triangle Midsegment Theorem Example 1 Continued Step 2 Compare the slopes

5 -4 The Triangle Midsegment Theorem Example 1 Continued Step 2 Compare the slopes of MN and XY. Since the slopes are the same, Holt Geometry

5 -4 The Triangle Midsegment Theorem Example 1 Continued Step 3 Compare the heights

5 -4 The Triangle Midsegment Theorem Example 1 Continued 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 Holt Geometry

5 -4 The Triangle Midsegment Theorem Example 2 A: Using the Triangle Midsegment Theorem

5 -4 The Triangle Midsegment Theorem Example 2 A: Using the Triangle Midsegment Theorem Find each measure. BD ∆ Midsegment Thm. Substitute 17 for AE. BD = 8. 5 Holt Geometry Simplify.

5 -4 The Triangle Midsegment Theorem Example 2 B: Using the Triangle Midsegment Theorem

5 -4 The Triangle Midsegment Theorem Example 2 B: Using the Triangle Midsegment Theorem Find each measure. m CBD ∆ Midsegment Thm. m CBD = m BDF Alt. Int. s Thm. m CBD = 26° Holt Geometry Substitute 26° for m BDF.

5 -4 The Triangle Midsegment Theorem Check It Out! Example 2 a Find each

5 -4 The Triangle Midsegment Theorem Check It Out! Example 2 a Find each measure. JL ∆ Midsegment Thm. 2(36) = JL 72 = JL Holt Geometry Substitute 36 for PN and multiply both sides by 2. Simplify.

5 -4 The Triangle Midsegment Theorem Check It Out! Example 2 b Find each

5 -4 The Triangle Midsegment Theorem Check It Out! Example 2 b Find each measure. PM ∆ Midsegment Thm. Substitute 97 for LK. PM = 48. 5 Simplify. Holt Geometry

5 -4 The Triangle Midsegment Theorem Check It Out! Example 2 c Find each

5 -4 The Triangle Midsegment Theorem Check It Out! Example 2 c Find each measure. m MLK ∆ Midsegment Thm. m MLK = m JMP Similar triangles m MLK = 102° Substitute. Holt Geometry

5 -4 The Triangle Midsegment Theorem Example 3: Indirect Measurement Application In an A-frame

5 -4 The Triangle Midsegment Theorem Example 3: 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? ∆ Midsegment Thm. Substitute 46 for PQ. ST = 23 Simplify. The length of the support ST is 23 inches. Holt Geometry

5 -4 The Triangle Midsegment Theorem Lesson Quiz: Part I Use the diagram for

5 -4 The Triangle Midsegment Theorem Lesson Quiz: Part I Use the diagram for Items 1– 3. Find each measure. 1. ED 10 2. AB 14 3. m BFE 44° Holt Geometry

5 -4 The Triangle Midsegment Theorem Lesson Quiz: Part II 4. Find the value

5 -4 The Triangle Midsegment Theorem Lesson Quiz: Part II 4. Find the value of n. 16 5. ∆XYZ is the midsegment triangle of ∆WUV. What is the perimeter of ∆XYZ? 11. 5 Holt Geometry

5 -4 The Triangle Midsegment Theorem Warm-Up Use the diagram for Items 1– 3.

5 -4 The Triangle Midsegment Theorem Warm-Up Use the diagram for Items 1– 3. Find each measure. 1. ED 10 2. AB 14 3. m BFE 44° Holt Geometry

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