GRADE 9
School
DAILY
Grade Level
19
Mary Mariette C. Escalante
Learning Area
MATHEMATICS
December 06-07, 2020
Quarter
3
Calamba National High SchoolAnnex
LESSON
Teacher
PLAN
Teaching Dates and
Time
I. OBJECTIVES
1. Content Standards
2. Performance
Standards
3. Learning
Competencies
Objectives
II. CONTENT
50 minutes
The learner demonstrates understanding of key concepts of parallelograms and triangle
similarity.
The learner is able to investigate, analyze, and solve problems involving parallelograms
and triangle similarity through appropriate and accurate representation.
The learners prove the condition for similarity of triangles.
Triangle Angle Bisector Theorem
At the end of the lesson the students are able to:
a) Define the triangle angle bisector theorem.
b) Find the unknown length of the side of the triangle.
c) Participate during the lesson.
Module 6: Similarity
Lesson: Triangle Angle Bisector Theorem
III. LEARNING
RESOURCES
A. References
1. Teacher’s Guide
pp 248-249
2. Learner’s
Materials
pp. 376-378
3. Textbook
Mathematics Learner’s Material 9
4. Additional
Materials from
Learning
Resources (LR)
portal
B. Other Learning
Resources
IV. PROCEDURES
TEACHER’S ACTIVITY
A. Reviewing previous lesson
or presenting the new lesson
1. What is our previous topic?
2. What are the Triangle similarity?
3. What is AAA Similarity Postulate?
4. What is AA Similarity Theorem?
5. What is SSS Similarity Theorem?
6. What is the SAS Similarity Theorem?
B. Establishing a purpose for
the lesson
Directions: Arrange the jumble words.
1. ATERLING
2. HERETOM
3. NOROPTIORO
4. ERTIBOCS
5. OARTI
6. GANEL
C. Presenting
examples/Instances of the
new lesson
Triangle Angle Bisector
-If a segment bisects an angle of a triangle,
then it divides the opposite side segments
proportional to the other two sides.
STUDENT’S ACTIVITY
1. Triangle Similarity.
2. AAA Similarity Postulate
AA Similarity Theorem
SSS Similarity Theorem
SAS Similarity Theorem.
3. AAA similarity postulate is two triangles
that has the same three angles.
4. AA similarity theorem is two triangles that
have the same two angles.
5. SSS similarity theorem is two triangles
that all the side are proportion to each
other.
5. SAS similarity theorem is two triangle
that has the same angles and have a
proportion of its two sides.
Answer:
1. TRIANGLE
2. THEOREM
3. PROPORTION
4. BISECTOR
5. RATIO
6. ANGEL
D. Discussing new concepts
and practicing new skills # 1
If: ̅̅̅̅
𝐻𝐷 𝑏𝑖𝑠𝑒𝑐𝑡𝑠 ∠𝐴𝐻𝐸
𝐷𝐴
𝐴𝐻
Then:
=
𝐷𝐸
𝐸𝐻
Solve for the unknown side applying the
Triangle Angle-Bisector Theorem.
1.
Solution.
𝐴𝐷
𝐷𝐵
=
𝐴𝐶
12
𝐵𝐶
𝑥
=
18
24
18x = 288
X = 16
2.
Solution.
3.
Solution:
𝑠
10−𝑠
=
6
9
9s = 60 – 6s
9s + 6s = 60
15s = 60
s=4
E. Discussing new concepts
and practicing new skills # 2
4.
Solution:
140 – 10s = 15s
140 = 15s + 10 s
140 = 25s
140
=s
25
𝑠=
2.
28
5
=5
3
5
You get the BZ by using Pythagorean
Theorem
a2 + b2 = c2
62 + 82 = c2
36 + 64 = c2
100 = c2
c = 10
BZ = 10
Next, set CU equal to x. UZ then becomes
8 – s. Set up the angle-bisector proportion
and solve for s:
𝐵𝐶
𝐶𝑈
=
𝐵𝑍
6
𝑍𝑈
𝑠
=
10
8−𝑠
48 – 6s = 10 s
48 = 10s + 6s
s=3
3.
Solution:
𝐶𝐷
𝐷𝐵
=
𝐴𝐶
𝑠
𝐴𝐵
40−𝑠
=
30
90
90s = 1200 – 300s
90s + 30s = 1200
120s = 1200
s = 10
40
F. Developing mastery
Seat Work:
Direction: Find the unknown side applying
the Triangle Angle-Bisector Theorem.
1.
Answer:
5
𝑥
1.
=
10
12
10𝑥 = 60
10𝑥
60
=
10
10
𝑥=6
5
6
=
10
1
=
I
2.
2.
24
x
G
18
H
3. The sides of a triangle are 𝟖, 𝟏𝟐,
and 𝟏𝟓. An angle bisector meets
the side of length 𝟏𝟓. Find the le
𝐼𝐹
6
24
1
=
3.
The perimeter of Δ𝑈𝑉𝑊 is 22 ½. ̅̅̅̅̅
𝑊𝑍
bisects ∠𝑈𝑊𝑉, 𝑈𝑍=2, and 𝑉𝑍=212. Find
UW and V
By the
angle bisector
2
theorem
=
2.5
𝐺𝐻
𝐼𝐻
12
48
1
4
4
15−𝑦
𝑦
=
12
180 − 12𝑦 = 8𝑦
180 = 8𝑦 + 12𝑦
180 = 20𝑦
180
20𝑦
=
20
20
𝑥=9
6
9
=
8
8
3
G. Finding practical
application of concepts and
skills in daily liv
2
=
=
24
𝑥
6𝑥 = 288
6𝑥
288
=
6
6
𝑥 = 48
6
12
=
6
F
2
𝐹𝐺
12
1
4
=
12
3
4
𝑈𝑊
so UW = 2x and VW = 2.5x for some
positive number of x. The perimeter of a
1
triangle is 22 so
2
2 + 2.5 + 2𝑥 + 2.5 = 22.5
4.5 + 4.5𝑥 = 22.5
4.5𝑥 = 18
𝑥=4
UW = 2x = 2(4) = 8
VW = 2.5 = 2.5 (4) = 10
1. What is our topic for today?
𝑉𝑊
H. Making generalizations
and abstractions about the
lesson
2. What is
Theorem?
Triangle
Angle
Bisector
3. What do you use to get angle bisector
theorem?
1. About Triangle Angle Bisector Theorem.
2. If a segment bisects an angle of a
triangle, then it divides the opposite side
segments proportional to the other two
sides.
3. Ratio and Proportion.
4. The unknown side of the triangle.
4. You use angle bisector theorem to find
what?
I. Evaluating learning
Quiz:
Direction: Solve for the unknown side of the
given triangle.
1. Find the value of x.
Answer:
𝐼𝐾
𝐻𝐾
1.
=
𝐼𝐺
𝑋
𝐺𝐻
30
=
24
40𝑥
40
720
=
40
40
𝑥 = 18
18
30
=
2. The sides of a triangle are 12, 16,
and 21. An angle bisector meets
the side of length 21. Find the
lengths x.
2.
3.
3. The sides of a triangle are 8, 12,
and 16. An angle bisector meets
the side of length 12. Find the
lengths x.
24
3
3
4
𝑥
4
1.
21−𝑥
12
3
16
3
4
𝑥
4
12−𝑥
=
=
8
16
16𝑥 = 96 + 8𝑥
16𝑥 + 8𝑥 = 96
24𝑥
96
=
24
24
𝑥=4
4
8
=
2
Direction: Find the unknown side of the
triangle.
40
=
12
16
16𝑥 = 252 − 12𝑥
16𝑥 + 12𝑥 = 252
28𝑥
252
=
28
28
𝑥=9
9
12
=
8
1
J. Additional activities for
application or remediation
=
=
16
1
2
Answer:
5
4𝑥+1
4.
=
3
15
3 (4𝑥 + 1) = 75
12𝑥 + 3 = 75
12𝑥 = 75 − 3
12𝑥 = 72
𝑥=6
5
4(6)+1
=
3
5
3
5
5.
=
=
3
𝐶𝐷
𝐶𝐴
10
15
15
25
15
5
3
𝐷𝐵
=
=
𝐵𝐴
20
𝐵𝐴
500
𝐵𝐴 =
10
BA= 50m
10
20
=
15
2
2.
6.
5
3
9
=
=
50
2
5
4
𝑥
3𝑥 = 36
3𝑥
36
=
3
3
𝑥 = 12
3
4
=
9
1
3
=
12
1
3
3.
V. REMARKS
VI. REFLECTION
A. No. of learners who
earned 80% in the evaluation
B. No. of learners who
require additional activities
for remediation who scored
below 80%
C. Did the remedial lessons
work? No. of learners who
have caught up with the
lesson
E. Which of my teaching
strategies worked well? Why
did these work?
F. What difficulties did I
encounter which my principal
or supervisor can help me
solve?
G. What innovation or
localized materials did I
use/discover which I wish to
share with other teachers?
There are _______ out of ________ students earned 80% in formative assessment.
There are _______ out of _________ students who earned below 80% and should be
given additional activities.
_________ YES (______ students)
___________ NO (__________students)