The Midline Theorem

1. MIDLINE THEOREM

2. Objectives:
• Explain Midline theorem
• Solve problem using Midline Theorem
• Patiently solve problems using midline theorem

3. Recall:
Midline Theorem: The segment
that joins the midpoints of two
sides of a triangle is parallel to
the third side and half as long.

4. Activity 1
Given: △ 𝐴𝐵𝐶 𝑎𝑛𝑑 𝑚𝑖𝑑𝑠𝑒𝑔𝑚𝑒𝑛𝑡 𝐷𝐸
Measure in cm the lengths of the three sides of
their triangle.
Locate the midpoints of each side and connect
them to form midsegments.
Measure the lengths of the midsegments and
compare them to half the lengths of the
corresponding sides.

5. Based on the activity;
1. How long is segment DE?
2. How long is segment AC?
3. Without using a ruler, is there
any method to solve midsegment of
a triangle? What is it?

6. The segment that joins the midpoints of two sides
of a triangle is parallel to the third side and half as
long.
𝐷𝐸 =
𝐴𝐶
2
A C
D E
B

7. Example:
M
A H
T
X
S
Refer to figure
1.If AH=20, what is XT?
2.If HS=15, what is ST?
3.If AX=12.5, what is SX?
4.Given that AH꞊20 and
HS꞊15, what is the area of
the triangle?
10
7.5
12.5

8. Recall:
A=
𝑏ℎ
2
b= 20 = (20)(15)/2
h= 15 = 300/2
= 150 sq. units

9. Group Activity: Gallery Walk
1. Each group will answer different problem.
2. Once you are done, post your output to your given
station.
3. Each group will have 1 member to remain in the station
to explain the output to the other groups.
4. I will count 1,2,3 then the members of each group will
travel counterclockwise direction until you will go back
to your own station.

10. Group 1:
Given: AI = 10.5
Questions:
1.What is MC?
2.How did you solve for MC?
21

11. Group 2:
Given: CG = 32
Questions:
1.What is GI?
2.How did you solve for GI?
16

12. Group 3:
Given: AG = 7 and CI = 8
Questions:
1.What is MG + CG?
2.How did you solve for the
sum?
30

13. Given: AI = 3x – 2 and MC = 9x - 13
Questions:
1.What is the value of x?
𝐴𝐼 =
𝑀𝐶
2
3𝑥 − 2 =
9𝑥 − 13
2
6𝑥 − 4 = 9𝑥 − 13
−4 + 13 = 9𝑥 − 6𝑥
9 = 3𝑥
9 =
3𝑥
3
3 = 𝑥

14. Given: AI = 3x – 2 and MC = 9x - 13
Questions:
2.How did you solve for x?
3.What is the sum of AI + MC? Why?
𝐴𝐼 = 3𝑥 − 2
3 3 − 2 = 7
𝑀𝐶 = 9𝑥 − 13
9 3 − 13 = 14
𝐴𝐼 + 𝑀𝐶 = 7 + 14 = 𝟐𝟏

15. Group 5:
Given: 𝑀𝐺 ≅ 𝐶𝐺, 𝐴𝐺 = 2𝑦 − 1 𝑎𝑛𝑑 𝐼𝐶 =
𝑦 + 5
Questions:
1.What is the value of y?
2.How did you solve for y?
2𝑦 − 1 = 𝑦 + 5
2𝑦 − 𝑦 = 5 + 1
𝒚 = 𝟔
3.How long are segments MG and CG? Why?
𝑴𝑮 = 𝟐𝟐
𝑪𝑮 = 𝟐𝟐
6

16. ASSESSMENT

17. Criteria Excellent(4) Satisfactory(3) Developing(2) Beginning(1)
Mathematical
Concept
Demonstrates a
thorough
understanding of
concepts.
Demonstrates a
adequate
understanding of
concepts.
Demonstrates a
incomplete
understanding of
concepts.
Shows lack of
understanding of
concepts.
Accuracy All information
provided is correct
and is logically
presented.
Most information
provided is correct.
Most information
provided is incorrect.
All of the information
provided is incorrect.
Organization of the
report
The flow of discussion
is smooth, logical, and
easy to understand.
The flow of discussion
is generally smooth,
logical, and easy to
understand.
The flow of discussion
is cluttered and can
hardly understand.
No logical
connections of ideas.
Presentation of the
output
Presents the work
intelligently, clearly,
and concisely.
Presents the work
clearly, and concisely.
Presents the work
adequately.
Presents the work
poorly.

18. Answer key:
1.x꞊1
2.AB꞊3
3.PR꞊6
4.QB꞊2.5
5.QR꞊5

19. Thank you for
listening!