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Geometry Warm-up Exercises

This warm-up exercise set covers finding midpoints, lengths, slopes, and applying the Triangle Midsegment Theorem in triangles. Includes step-by-step examples and a quiz.

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Geometry Warm-up Exercises

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  1. 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. 3.Find the slope of AB. 4.What is the slope of a line parallel to 3x + 2y = 12? (3, 5) 5 0

  2. 5-4 The Triangle Midsegment Theorem Holt Geometry

  3. 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.

  4. 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.

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

  6. Step 3 Compare the heights of MN and XY. Example 1 Continued

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

  8. 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.

  9. 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.

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

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

  12. 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.

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

  14. 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

  15. Warm-Up Use the diagram for Items 1–3. Find each measure. 1.ED 2.AB 3. mBFE 10 14 44°

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