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 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