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Geometry The Triangle Midsegment Theorem

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rhonda
28 diapositives · 664 Views · Aug 27, 2014

Geometry The Triangle Midsegment Theorem. Warm up. Find each length. 1) NX 2) MR 3) NP. P. 1). S. 3. R. X. 4.5. 5.5. M. Q. N. The Triangle Midsegment Theorem.

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Geometry The Triangle Midsegment Theorem
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  1. Geometry The Triangle Midsegment Theorem CONFIDENTIAL

  2. Warm up Find each length. 1) NX 2) MR 3) NP P 1) S 3 R X 4.5 5.5 M Q N CONFIDENTIAL

  3. 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 midsegment, which form the midsegment triangle. Q Y X P R Z CONFIDENTIAL

  4. Examining Midsegments in the coordinate Plane y H(-5, 6) 6 L 4 J(1, 2) K 2 0 x -2 -2 G(-7, -2) Next Page: CONFIDENTIAL

  5. y H(-5, 6) 6 L 4 J(1, 2) K 2 0 x -2 -2 G(-7, -2) Next Page: CONFIDENTIAL

  6. y H(-5, 6) 6 L 4 J(1, 2) K 2 0 x -2 -2 G(-7, -2) CONFIDENTIAL

  7. Now you try! CONFIDENTIAL

  8. The relationship show in Example 1 is true for the three midsegments of every triangle . CONFIDENTIAL

  9. Triangle Midsegment Theorem Theorem 4.1 A Midsegment of a triangle is parallel to a side of the triangle, and its length is half the length of that side. B D E A C CONFIDENTIAL

  10. Using the triangle Midsegment Theorem Find each measure. S U A) UW 5.2 R 41˚ ∆ Midsegment Thm. Substitute 7.4 for ST. Simplify. V 7.4 W T Next Page: CONFIDENTIAL

  11. S B) m/ SVU U 5.2 R 41˚ V 7.4 ∆ Midsegment Thm. Alt. Int. /s Thm. Substitute 41˚ for m/ VUW. W T CONFIDENTIAL

  12. Now you try! 2) Find each measure. a) JL b) PM c) m/ MLK P K J 36 102˚ M N • 72 • b) 43.5 • c)1020 97 L CONFIDENTIAL

  13. 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? C ∆ midsegment Thm. Substitute 775 foe BD. Multiply both sides by 2. 920 m 700 m 775 m B D 920 m 700 m E A The distance AE across the base of the volcano is about 1550 meters. CONFIDENTIAL

  14. Now you try! 3) Suppose Anna’s result in Example 3 is correct to check it, she measures a second triangle. How many meters will she measure between H and F? E A 640 m 1005 m H F 3) 640 m 1005 m G CONFIDENTIAL

  15. Now some problems for you to practice ! CONFIDENTIAL

  16. Assessment CONFIDENTIAL

  17. Find each measure. • 2) NM 3) XZ • 4) NZ 5) m/ LMN • 6) m/ YXZ 7) m/ XLM Y 10.2 L 5.6 M 2) 5.1 3) 11.2 4) 5.6 5)290 6)290 7)290 29˚ X Z N CONFIDENTIAL

  18. 8) In this A-frame house, the width of the first floor XZ is 30 feet. The second floor CD is slightly above and parallel to the midsegment of ∆XYZ. Is the width of the second floor more or less than 5 yards? Explain. Y C D X Z CONFIDENTIAL

  19. Let’s review 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 midsegment, which form the midsegment triangle. Q Y X P R Z CONFIDENTIAL

  20. Examining Midsegments in the coordinate Plane y H(-5, 6) 6 L 4 J(1, 2) K 2 0 x -2 -2 G(-7, -2) Next Page: CONFIDENTIAL

  21. y H(-5, 6) 6 L 4 J(1, 2) K 2 0 x -2 -2 G(-7, -2) Next Page: CONFIDENTIAL

  22. y H(-5, 6) 6 L 4 J(1, 2) K 2 0 x -2 -2 G(-7, -2) CONFIDENTIAL

  23. The relationship show in Example 1 is true for the three midsegments of every triangle . CONFIDENTIAL

  24. Theorem 4.1 Triangle Midsegment Theorem A Midsegment of a triangle is parallel to a side of the triangle, and its length is half the length of that side. B D E A C CONFIDENTIAL

  25. Using the triangle Midsegment Theorem Find each measure. S U A) UW 5.2 R 41˚ ∆ Midsegment Thm. Substitute 7.4 for ST. Simplify. V 7.4 W T Next Page: CONFIDENTIAL

  26. S B) m/ SVU U 5.2 R 41˚ V 7.4 ∆ Midsegment Thm. Alt. Int. /s Thm. Substitute 41˚ for m/ VUW. W T CONFIDENTIAL

  27. 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? C ∆ midsegment Thm. Substitute 775 foe BD. Multiply both sides by 2. 920 m 700 m 775 m B D 920 m 700 m E The distance AE across the base of the volcano is about 1550 meters. A CONFIDENTIAL

  28. You did a great job today! CONFIDENTIAL