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THE MIDLINE
THEOREM
MIDLINE THEOREM
οƒ’The segment that joins the
midpoints of two sides of a
triangle is parallel to the third
side and half as...
A
B C
D E
In βˆ†ABC, D and E are the midpoints of 𝐴𝐡
and 𝐴𝐢 respectively.
Complete the following
statements:
 DE = ______
...
In βˆ†ABC, D and E are the midpoints of 𝐴𝐡
and 𝐡𝐢 respectively.
Fill in the blanks.
1. If DE = 12, then AC =
_____.
2. If AC...
In βˆ†MCG, A and I are the midpoints of 𝑀𝐺
and 𝐺𝐢 respectively.
M C
G
A I
Given: AI = 3x – 2
CM = 9x – 13
Question: How long...
CHOOSE A BRIEFCASE
QUIZ
In βˆ†DOG, B and E are the midpoints of
𝐷𝑂 and 𝐷𝐺 respectively.
B
O G
D
E
If DE = 13, then
𝟏
𝟐
DG =
_____
TIME IS
UP!!!
13
In βˆ†DOG, B and E are the midpoints of
𝐷𝑂 and 𝐷𝐺 respectively.
B
O G
D
E
TIME IS
UP!!!
51
If BE = 17, then BE + OG =
_____
In βˆ†DOG, B and E are the midpoints of
𝐷𝑂 and 𝐷𝐺 respectively.
B
O G
D
E
Given: BE = 2x + 5
OG = 5x + 6
Question: How long ...
In βˆ†DOG, B and E are the midpoints of
𝐷𝑂 and 𝐷𝐺 respectively.
B
O G
D
E
TIME IS
UP!!!
6
If OG = 36, then
𝟏
πŸ‘
BE =
_____
In βˆ†DOG, B and E are the midpoints of
𝐷𝑂 and 𝐷𝐺 respectively.
B
O G
D
E
Given: BD = 3a + 3
BO = 7a - 21
Question: How long...
In βˆ†DOG, B and E are the midpoints of
𝐷𝑂 and 𝐷𝐺 respectively.
B
O G
D
E
TIME IS
UP!!!
11
If DO = 44, then
𝟏
𝟐
BD =
_____
In βˆ†DOG, B and E are the midpoints of
𝐷𝑂 and 𝐷𝐺 respectively.
B
O G
D
E
Given: DE = 2y + 1
EG = 3y - 7
Question: How long ...
In βˆ†DOG, B and E are the midpoints of
𝐷𝑂 and 𝐷𝐺 respectively.
B
O G
D
E
TIME IS
UP!!!
12
If BE = 6, then GO =
_____.
In βˆ†DOG, B and E are the midpoints of
𝐷𝑂 and 𝐷𝐺 respectively.
B
O G
D
E
Given: BE = 4b - 7
GO = 5b - 5
Question: How long ...
In βˆ†DOG, B and E are the midpoints of
𝐷𝑂 and 𝐷𝐺 respectively.
B
O G
D
E
TIME IS
UP!!!
45
If OB = 15, and GE = 13,
then DO ...
Let’s see how well
did you understand
our lesson.
Short Quiz
In βˆ†LUV, B and E are the midpoints of πΏπ‘ˆ and
𝐿𝑉 respectively.
B
U V
L
E
If LE = 19, then
𝟏
𝟐
LV =
_____
1
B
U V
L
E
If BE = 21, then BE + UV =
_____
In βˆ†LUV, B and E are the midpoints of πΏπ‘ˆ and
𝐿𝑉 respectively.
2
B
U V
L
E
Given: BE = 2x - 1
UV = x + 4
Question: How long is
BE?
In βˆ†LUV, B and E are the midpoints of πΏπ‘ˆ and
𝐿𝑉 respecti...
B
U V
L
E
If UV = 32, then
𝟏
πŸ’
BE =
_____
In βˆ†LUV, B and E are the midpoints of πΏπ‘ˆ and
𝐿𝑉 respectively.
4
B
U V
L
E
Given: BL = 2a - 1
BU = 4a - 17
Question: How long is
BU?
In βˆ†LUV, B and E are the midpoints of πΏπ‘ˆ and
𝐿𝑉 respec...
B
U V
L
E
If LU = 56, then
𝟏
𝟐
BL =
_____
In βˆ†LUV, B and E are the midpoints of πΏπ‘ˆ and
𝐿𝑉 respectively.
6
B
U V
L
E
Given: EL = 2y + 14
EV = 5y - 16
Question: How long is
EV?
In βˆ†LUV, B and E are the midpoints of πΏπ‘ˆ and
𝐿𝑉 respe...
B
U V
L
E
If BE = 13.8, then UV =
_____.
In βˆ†LUV, B and E are the midpoints of πΏπ‘ˆ and
𝐿𝑉 respectively.
8
B
U V
L
E
Given: BE = 3b - 7
UV = 4b + 8
Question: How long is
UV?
In βˆ†LUV, B and E are the midpoints of πΏπ‘ˆ and
𝐿𝑉 respect...
B
U V
L
E
If BU = 17, and EV = 14,
then LU + LV = _____.
In βˆ†LUV, B and E are the midpoints of πΏπ‘ˆ and
𝐿𝑉 respectively.
10
ANSWERS
In βˆ†LUV, B and E are the midpoints of πΏπ‘ˆ and
𝐿𝑉 respectively.
B
U V
L
E
If LE = 19, then
𝟏
𝟐
LV =
_____
1
19
B
U V
L
E
If BE = 21, then BE + UV =
_____
In βˆ†LUV, B and E are the midpoints of πΏπ‘ˆ and
𝐿𝑉 respectively.
2
63
B
U V
L
E
Given: BE = 2x - 1
UV = x + 4
Question: How long is
BE?
In βˆ†LUV, B and E are the midpoints of πΏπ‘ˆ and
𝐿𝑉 respecti...
B
U V
L
E
If UV = 32, then
𝟏
πŸ’
BE =
_____
In βˆ†LUV, B and E are the midpoints of πΏπ‘ˆ and
𝐿𝑉 respectively.
4
4
B
U V
L
E
Given: BL = 2a - 1
BU = 4a - 17
Question: How long is
BU?
In βˆ†LUV, B and E are the midpoints of πΏπ‘ˆ and
𝐿𝑉 respec...
B
U V
L
E
If LU = 56, then
𝟏
𝟐
BL =
_____
In βˆ†LUV, B and E are the midpoints of πΏπ‘ˆ and
𝐿𝑉 respectively.
6
14
B
U V
L
E
Given: EL = 2y + 14
EV = 5y - 16
Question: How long is
EV?
In βˆ†LUV, B and E are the midpoints of πΏπ‘ˆ and
𝐿𝑉 respe...
B
U V
L
E
If BE = 13.8, then UV =
_____.
In βˆ†LUV, B and E are the midpoints of πΏπ‘ˆ and
𝐿𝑉 respectively.
8
27.6
B
U V
L
E
Given: BE = 3b - 7
UV = 4b + 8
Question: How long is
UV?
In βˆ†LUV, B and E are the midpoints of πΏπ‘ˆ and
𝐿𝑉 respect...
B
U V
L
E
If BU = 17, and EV = 14,
then LU + LV = _____.
In βˆ†LUV, B and E are the midpoints of πΏπ‘ˆ and
𝐿𝑉 respectively.
10
...
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Midline theorem - Mathematics - Geometry

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*Fun Activities
*Short Quiz

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Midline theorem - Mathematics - Geometry

  1. 1. THE MIDLINE THEOREM
  2. 2. MIDLINE THEOREM οƒ’The segment that joins the midpoints of two sides of a triangle is parallel to the third side and half as long.
  3. 3. A B C D E In βˆ†ABC, D and E are the midpoints of 𝐴𝐡 and 𝐴𝐢 respectively. Complete the following statements:  DE = ______  AD = ______  AE = ______ 𝟏 𝟐 BC BD CE
  4. 4. In βˆ†ABC, D and E are the midpoints of 𝐴𝐡 and 𝐡𝐢 respectively. Fill in the blanks. 1. If DE = 12, then AC = _____. 2. If AC =42, then DE = _____. 3. If AD = 7, then AB = _____. 4. If BC = 36, then BE = _____. 5. If BD = 8 and EC = 9, then AB + BC = _____. D A C B E 24 21 14 18 34 15
  5. 5. In βˆ†MCG, A and I are the midpoints of 𝑀𝐺 and 𝐺𝐢 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. 6. CHOOSE A BRIEFCASE QUIZ
  7. 7. In βˆ†DOG, B and E are the midpoints of 𝐷𝑂 and 𝐷𝐺 respectively. B O G D E If DE = 13, then 𝟏 𝟐 DG = _____ TIME IS UP!!! 13
  8. 8. In βˆ†DOG, B and E are the midpoints of 𝐷𝑂 and 𝐷𝐺 respectively. B O G D E TIME IS UP!!! 51 If BE = 17, then BE + OG = _____
  9. 9. In βˆ†DOG, B and E are the midpoints of 𝐷𝑂 and 𝐷𝐺 respectively. B O G D E Given: BE = 2x + 5 OG = 5x + 6 Question: How long is BE? TIME IS UP!!! 13
  10. 10. In βˆ†DOG, B and E are the midpoints of 𝐷𝑂 and 𝐷𝐺 respectively. B O G D E TIME IS UP!!! 6 If OG = 36, then 𝟏 πŸ‘ BE = _____
  11. 11. In βˆ†DOG, B and E are the midpoints of 𝐷𝑂 and 𝐷𝐺 respectively. B O G D E Given: BD = 3a + 3 BO = 7a - 21 Question: How long is BO? TIME IS UP!!! 21
  12. 12. In βˆ†DOG, B and E are the midpoints of 𝐷𝑂 and 𝐷𝐺 respectively. B O G D E TIME IS UP!!! 11 If DO = 44, then 𝟏 𝟐 BD = _____
  13. 13. In βˆ†DOG, B and E are the midpoints of 𝐷𝑂 and 𝐷𝐺 respectively. B O G D E Given: DE = 2y + 1 EG = 3y - 7 Question: How long is EG? TIME IS UP!!! 17
  14. 14. In βˆ†DOG, B and E are the midpoints of 𝐷𝑂 and 𝐷𝐺 respectively. B O G D E TIME IS UP!!! 12 If BE = 6, then GO = _____.
  15. 15. In βˆ†DOG, B and E are the midpoints of 𝐷𝑂 and 𝐷𝐺 respectively. B O G D E Given: BE = 4b - 7 GO = 5b - 5 Question: How long is GO? TIME IS UP!!! 10
  16. 16. In βˆ†DOG, B and E are the midpoints of 𝐷𝑂 and 𝐷𝐺 respectively. B O G D E TIME IS UP!!! 45 If OB = 15, and GE = 13, then DO + BD = _____.
  17. 17. Let’s see how well did you understand our lesson. Short Quiz
  18. 18. In βˆ†LUV, B and E are the midpoints of πΏπ‘ˆ and 𝐿𝑉 respectively. B U V L E If LE = 19, then 𝟏 𝟐 LV = _____ 1
  19. 19. B U V L E If BE = 21, then BE + UV = _____ In βˆ†LUV, B and E are the midpoints of πΏπ‘ˆ and 𝐿𝑉 respectively. 2
  20. 20. B U V L E Given: BE = 2x - 1 UV = x + 4 Question: How long is BE? In βˆ†LUV, B and E are the midpoints of πΏπ‘ˆ and 𝐿𝑉 respectively. 3
  21. 21. B U V L E If UV = 32, then 𝟏 πŸ’ BE = _____ In βˆ†LUV, B and E are the midpoints of πΏπ‘ˆ and 𝐿𝑉 respectively. 4
  22. 22. B U V L E Given: BL = 2a - 1 BU = 4a - 17 Question: How long is BU? In βˆ†LUV, B and E are the midpoints of πΏπ‘ˆ and 𝐿𝑉 respectively. 5
  23. 23. B U V L E If LU = 56, then 𝟏 𝟐 BL = _____ In βˆ†LUV, B and E are the midpoints of πΏπ‘ˆ and 𝐿𝑉 respectively. 6
  24. 24. B U V L E Given: EL = 2y + 14 EV = 5y - 16 Question: How long is EV? In βˆ†LUV, B and E are the midpoints of πΏπ‘ˆ and 𝐿𝑉 respectively. 7
  25. 25. B U V L E If BE = 13.8, then UV = _____. In βˆ†LUV, B and E are the midpoints of πΏπ‘ˆ and 𝐿𝑉 respectively. 8
  26. 26. B U V L E Given: BE = 3b - 7 UV = 4b + 8 Question: How long is UV? In βˆ†LUV, B and E are the midpoints of πΏπ‘ˆ and 𝐿𝑉 respectively. 9
  27. 27. B U V L E If BU = 17, and EV = 14, then LU + LV = _____. In βˆ†LUV, B and E are the midpoints of πΏπ‘ˆ and 𝐿𝑉 respectively. 10
  28. 28. ANSWERS
  29. 29. In βˆ†LUV, B and E are the midpoints of πΏπ‘ˆ and 𝐿𝑉 respectively. B U V L E If LE = 19, then 𝟏 𝟐 LV = _____ 1 19
  30. 30. B U V L E If BE = 21, then BE + UV = _____ In βˆ†LUV, B and E are the midpoints of πΏπ‘ˆ and 𝐿𝑉 respectively. 2 63
  31. 31. B U V L E Given: BE = 2x - 1 UV = x + 4 Question: How long is BE? In βˆ†LUV, B and E are the midpoints of πΏπ‘ˆ and 𝐿𝑉 respectively. 3 3
  32. 32. B U V L E If UV = 32, then 𝟏 πŸ’ BE = _____ In βˆ†LUV, B and E are the midpoints of πΏπ‘ˆ and 𝐿𝑉 respectively. 4 4
  33. 33. B U V L E Given: BL = 2a - 1 BU = 4a - 17 Question: How long is BU? In βˆ†LUV, B and E are the midpoints of πΏπ‘ˆ and 𝐿𝑉 respectively. 5 15
  34. 34. B U V L E If LU = 56, then 𝟏 𝟐 BL = _____ In βˆ†LUV, B and E are the midpoints of πΏπ‘ˆ and 𝐿𝑉 respectively. 6 14
  35. 35. B U V L E Given: EL = 2y + 14 EV = 5y - 16 Question: How long is EV? In βˆ†LUV, B and E are the midpoints of πΏπ‘ˆ and 𝐿𝑉 respectively. 7 34
  36. 36. B U V L E If BE = 13.8, then UV = _____. In βˆ†LUV, B and E are the midpoints of πΏπ‘ˆ and 𝐿𝑉 respectively. 8 27.6
  37. 37. B U V L E Given: BE = 3b - 7 UV = 4b + 8 Question: How long is UV? In βˆ†LUV, B and E are the midpoints of πΏπ‘ˆ and 𝐿𝑉 respectively. 9 52
  38. 38. B U V L E If BU = 17, and EV = 14, then LU + LV = _____. In βˆ†LUV, B and E are the midpoints of πΏπ‘ˆ and 𝐿𝑉 respectively. 10 62
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Midline Theorem *Fun Activities *Short Quiz

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