Midline theorem - Mathematics - Geometry
38
THE MIDLINE THEOREM
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Transcript of Midline theorem - Mathematics - Geometry
THE MIDLINE THEOREM
MIDLINE THEOREM The segment that joins the midpoints of two sides of a triangle is parallel to the third side and half as long.
A
B C
D E
In ∆ABC, D and E are the midpoints of and respectively.Complete the following statements:
DE = ______
AD = ______
AE = ______
BC
BDCE
In ∆ABC, D and E are the midpoints of and 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 = _____.6. If DE = 5, then DE + AC
= _____.
D
A C
B
E
2421141834
15
In ∆MCG, A and I are the midpoints of and respectively.
M C
G
A I
Given: AI = 3x – 2CM = 9x – 13
Question: How long is CM?Given: AG = 2y - 1
AM = y + 5Question: How long is AG?
CHOOSE A BRIEFCASE
QUIZ
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
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 = _____
In ∆DOG, B and E are the midpoints of and respectively.
B
O G
D
E
Given: BE = 2x + 5OG = 5x + 6
Question: How long is BE?
TIME IS UP!!!
13
In ∆DOG, B and E are the midpoints of and respectively.
B
O G
D
E
TIME IS UP!!!
6
If OG = 36, then = _____
In ∆DOG, B and E are the midpoints of and respectively.
B
O G
D
E
Given: BD = 3a + 3BO = 7a - 21
Question: How long is BO?
TIME IS UP!!!
21
In ∆DOG, B and E are the midpoints of and respectively.
B
O G
D
E
TIME IS UP!!!
11
If DO = 44, then = _____
In ∆DOG, B and E are the midpoints of and respectively.
B
O G
D
E
Given: DE = 2y + 1EG = 3y - 7
Question: How long is EG?
TIME IS UP!!!
17
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 = _____.
In ∆DOG, B and E are the midpoints of and respectively.
B
O G
D
E
Given: BE = 4b - 7GO = 5b - 5
Question: How long is GO?
TIME IS UP!!!
10
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 = _____.
Let’s see how well did you understand
our lesson.
Short Quiz
In ∆LUV, B and E are the midpoints of and respectively.
B
U V
L
E
If LE = 19, then = _____
1
B
U V
L
E
If BE = 21, then BE + UV = _____
In ∆LUV, B and E are the midpoints of and respectively.
2
B
U V
L
E
Given: BE = 2x - 1UV = x + 4
Question: How long is BE?
In ∆LUV, B and E are the midpoints of and respectively.
3
B
U V
L
E
If UV = 32, then = _____
In ∆LUV, B and E are the midpoints of and respectively.
4
B
U V
L
E
Given: BL = 2a - 1BU = 4a - 17
Question: How long is BU?
In ∆LUV, B and E are the midpoints of and respectively.
5
B
U V
L
E
If LU = 56, then = _____
In ∆LUV, B and E are the midpoints of and respectively.
6
B
U V
L
E
Given: EL = 2y + 14EV = 5y - 16
Question: How long is EV?
In ∆LUV, B and E are the midpoints of and respectively.
7
B
U V
L
E
If BE = 13.8, then UV = _____.
In ∆LUV, B and E are the midpoints of and respectively.
8
B
U V
L
E
Given: BE = 3b - 7UV = 4b + 8
Question: How long is UV?
In ∆LUV, B and E are the midpoints of and respectively.
9
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
ANSWERS
In ∆LUV, B and E are the midpoints of and respectively.
B
U V
L
E
If LE = 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
63
B
U V
L
E
Given: BE = 2x - 1UV = x + 4
Question: How long is BE?
In ∆LUV, B and E are the midpoints of and respectively.
3
3
B
U V
L
E
If UV = 32, then = _____
In ∆LUV, B and E are the midpoints of and respectively.
4
4
B
U V
L
E
Given: BL = 2a - 1BU = 4a - 17
Question: How long is BU?
In ∆LUV, B and E are the midpoints of and respectively.
5
15
B
U V
L
E
If LU = 56, then = _____
In ∆LUV, B and E are the midpoints of and respectively.
6
14
B
U V
L
E
Given: EL = 2y + 14EV = 5y - 16
Question: How long is EV?
In ∆LUV, B and E are the midpoints of and respectively.
7
34
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
B
U V
L
E
Given: BE = 3b - 7UV = 4b + 8
Question: How long is UV?
In ∆LUV, B and E are the midpoints of and respectively.
9
52
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
