Midline theorem - Mathematics - Geometry

Midline Theorem
*Fun Activities
*Short Quiz

1. THE MIDLINE THEOREM

2. Midline theorem The segment that joins the midpoints of two sides of a triangle is parallel to the third side and half as long.

3. A B C D E In ∆ABC, D and E are the midpoints of and respectively.   Complete the following statements: DE = ______ AD = ______ AE = ______ BC   BD CE

4. In ∆ABC, D and E are the midpoints of and respectively.   Fill in the blanks. If DE = 12, then AC = _____. If AC =42, then DE = _____. If AD = 7, then AB = _____. If BC = 36, then BE = _____. If BD = 8 and EC = 9, then AB + BC = _____. If DE = 5, then DE + AC = _____. D A C B E 24 21 1 4 18 3 4 15

5. In ∆MCG, A and I are the midpoints of and respectively.   M C G A I Given: AI = 3x – 2 CM = 9x – 13 Question: How long is CM? Given: AG = 2y - 1 AM = y + 5 Question: How long is AG?

6. 9 Choose a briefcase 10 8 7 6 3 1 5 4 2 QUIZ

7. In ∆DOG, B and E are the midpoints of and respectively.   B O G D E If DE = 13, then DG = _____   TIME IS UP!!! 13

8. In ∆DOG, B and E are the midpoints of and respectively.   B O G D E TIME IS UP!!! 51 If BE = 17, then BE + OG = _____

9. In ∆DOG, B and E are the midpoints of and respectively.   B O G D E Given: BE = 2x + 5 OG = 5x + 6 Question: How long is BE? TIME IS UP!!! 13

10. In ∆DOG, B and E are the midpoints of and respectively.   B O G D E TIME IS UP!!! 6 If OG = 36, then = _____  

11. In ∆DOG, B and E are the midpoints of and respectively.   B O G D E Given: BD = 3a + 3 BO = 7a - 21 Question: How long is BO? TIME IS UP!!! 21

12. In ∆DOG, B and E are the midpoints of and respectively.   B O G D E TIME IS UP!!! 11 If DO = 44, then = _____  

13. In ∆DOG, B and E are the midpoints of and respectively.   B O G D E Given: DE = 2y + 1 EG = 3y - 7 Question: How long is EG? TIME IS UP!!! 17

14. In ∆DOG, B and E are the midpoints of and respectively.   B O G D E TIME IS UP!!! 12 If BE = 6, then GO = _____.

15. In ∆DOG, B and E are the midpoints of and respectively.   B O G D E Given: BE = 4b - 7 GO = 5b - 5 Question: How long is GO? TIME IS UP!!! 10

16. In ∆DOG, B and E are the midpoints of and respectively.   B O G D E TIME IS UP!!! 45 If OB = 15, and GE = 13, then DO + BD = _____.

17. Let’s see how well did you understand our lesson. Short Quiz

18. In ∆LUV, B and E are the midpoints of and respectively.   B U V L E If L E = 19, then = _____   1

19. B U V L E If BE = 21, then BE + UV = _____ In ∆LUV, B and E are the midpoints of and respectively.   2

20. B U V L E Given: BE = 2x - 1 UV = x + 4 Question: How long is BE? In ∆LUV, B and E are the midpoints of and respectively.   3

21. B U V L E If UV = 32, then = _____   In ∆LUV, B and E are the midpoints of and respectively.   4

22. B U V L E Given: BL = 2a - 1 BU = 4a - 17 Question: How long is BU? In ∆LUV, B and E are the midpoints of and respectively.   5

23. B U V L E If LU = 56, then = _____   In ∆LUV, B and E are the midpoints of and respectively.   6

24. B U V L E Given: EL = 2y + 14 EV = 5y - 16 Question: How long is EV? In ∆LUV, B and E are the midpoints of and respectively.   7

25. B U V L E If BE = 13.8, then UV = _____. In ∆LUV, B and E are the midpoints of and respectively.   8

26. B U V L E Given: BE = 3b - 7 UV = 4b + 8 Question: How long is UV? In ∆LUV, B and E are the midpoints of and respectively.   9

27. B U V L E If BU = 17, and EV = 14, then LU + LV = _____. In ∆LUV, B and E are the midpoints of and respectively.   10

28. ANSWERS

29. In ∆LUV, B and E are the midpoints of and respectively.   B U V L E If L E = 19, then = _____   1 19

30. B U V L E If BE = 21, then BE + UV = _____ In ∆LUV, B and E are the midpoints of and respectively.   2 63

31. B U V L E Given: BE = 2x - 1 UV = x + 4 Question: How long is BE? In ∆LUV, B and E are the midpoints of and respectively.   3 3

32. B U V L E If UV = 32, then = _____   In ∆LUV, B and E are the midpoints of and respectively.   4 4

33. B U V L E Given: BL = 2a - 1 BU = 4a - 17 Question: How long is BU? In ∆LUV, B and E are the midpoints of and respectively.   5 1 5

34. B U V L E If LU = 56, then = _____   In ∆LUV, B and E are the midpoints of and respectively.   6 14

35. B U V L E Given: EL = 2y + 14 EV = 5y - 16 Question: How long is EV? In ∆LUV, B and E are the midpoints of and respectively.   7 34

36. B U V L E If BE = 13.8, then UV = _____. In ∆LUV, B and E are the midpoints of and respectively.   8 27.6

37. B U V L E Given: BE = 3b - 7 UV = 4b + 8 Question: How long is UV? In ∆LUV, B and E are the midpoints of and respectively.   9 52

38. B U V L E If BU = 17, and EV = 14, then LU + LV = _____. In ∆LUV, B and E are the midpoints of and respectively.   10 62