The document explains the midline theorem in geometry. The midline theorem states that the segment joining the midpoints of two sides of a triangle is parallel to the third side and half its length. The document provides examples of applying the midline theorem to solve for unknown lengths in various triangles. It also includes a short quiz testing understanding of using the midline theorem.

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 𝐴𝐵
and 𝐴𝐶 respectively.
Complete the following
statements:
 DE = ______
 AD = ______
 AE = ______
𝟏
𝟐
BC
BD
CE

4. In ∆ABC, D and E are the midpoints of 𝐴𝐵
and 𝐵𝐶 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. In ∆MCG, A and I are the midpoints of 𝑀𝐺
and 𝐺𝐶 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. CHOOSE A BRIEFCASE
QUIZ

7. In ∆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. In ∆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. In ∆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. In ∆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
𝟑
BE =
_____

11. In ∆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. In ∆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. In ∆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. In ∆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. In ∆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. In ∆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. Let’s see how well
did you understand
our lesson.
Short Quiz

18. In ∆LUV, B and E are the midpoints of 𝐿𝑈 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 ∆LUV, B and E are the midpoints of 𝐿𝑈 and
𝐿𝑉 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 𝐿𝑈 and
𝐿𝑉 respectively.
3

21. B
U V
L
E
If UV = 32, then
𝟏
𝟒
BE =
_____
In ∆LUV, B and E are the midpoints of 𝐿𝑈 and
𝐿𝑉 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 𝐿𝑈 and
𝐿𝑉 respectively.
5

23. B
U V
L
E
If LU = 56, then
𝟏
𝟐
BL =
_____
In ∆LUV, B and E are the midpoints of 𝐿𝑈 and
𝐿𝑉 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 𝐿𝑈 and
𝐿𝑉 respectively.
7

25. B
U V
L
E
If BE = 13.8, then UV =
_____.
In ∆LUV, B and E are the midpoints of 𝐿𝑈 and
𝐿𝑉 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 𝐿𝑈 and
𝐿𝑉 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 𝐿𝑈 and
𝐿𝑉 respectively.
10

28. ANSWERS

29. In ∆LUV, B and E are the midpoints of 𝐿𝑈 and
𝐿𝑉 respectively.
B
U V
L
E
If LE = 19, then
𝟏
𝟐
LV =
_____
1
19

30. B
U V
L
E
If BE = 21, then BE + UV =
_____
In ∆LUV, B and E are the midpoints of 𝐿𝑈 and
𝐿𝑉 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 𝐿𝑈 and
𝐿𝑉 respectively.
3
3

32. B
U V
L
E
If UV = 32, then
𝟏
𝟒
BE =
_____
In ∆LUV, B and E are the midpoints of 𝐿𝑈 and
𝐿𝑉 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 𝐿𝑈 and
𝐿𝑉 respectively.
5
15

34. B
U V
L
E
If LU = 56, then
𝟏
𝟐
BL =
_____
In ∆LUV, B and E are the midpoints of 𝐿𝑈 and
𝐿𝑉 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 𝐿𝑈 and
𝐿𝑉 respectively.
7
34

36. B
U V
L
E
If BE = 13.8, then UV =
_____.
In ∆LUV, B and E are the midpoints of 𝐿𝑈 and
𝐿𝑉 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 𝐿𝑈 and
𝐿𝑉 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 𝐿𝑈 and
𝐿𝑉 respectively.
10
62