MATHEMATICS LESSON PLAN
GRADE 9
TERM 2: APRIL - JUNE 2015
PROVINCE:
DISTRICT:
SCHOOL:
TEACHER’S NAME:
DATE:
DURATION:
1 Hour
1. TOPIC: GEOMETRY OF 2D-SHAPES: SOLVING PROBLEMS (Lesson 8)
2. CONCEPTS & SKILLS TO BE ACHIEVED:
By the end of the lesson learners should know and be able to solve geometric problems
involving unknown sides and angles in triangles and quadrilaterals, using known properties
of triangles and quadrilaterals, as well as properties of similar triangles.
Grade 9 Lesson Plan: 1+4 Intervention – Term 2
(Draft)
3. RESOURCES:
DBE Workbook, Sasol-Inzalo Workbook, textbooks
4. PRIOR KNOWLEDGE:


minimum conditions for similar triangles
solving of equations
5. REVIEW AND CORRECTION OF HOMEWORK (suggested time: 10 minutes)
Homework provides an opportunity for teachers to track learners’ progress in the mastery of
mathematics concepts and to identify the problematic areas which require immediate attention.
Therefore it is recommended that you place more focus on addressing errors from learner
responses that may later become misconceptions.
6. INTRODUCTION (Suggested time: 10 Minutes)
Activity 1
Ask learners to list the conditions for similarity of triangles.
Activity 2
Discuss with learners the notation of similar triangles.
A
*
D
*
B
*
*
C E
*
* F
The correct notation is very important when naming the similarity between triangles. For example,
̂=D
̂,
the notation for the triangles above should be: Δ ABC /// Δ DEF, because it indicates that A
̂=E
̂ , Ĉ = F̂ and AB = BC = AC
B
DE
EF
DF
Grade 9 Lesson Plan: 1+4 Intervention – Term 2
(Draft)
Page 2 of 5
7. LESSON PRESENTATION/DEVELOPMENT (Suggested time: 20 minutes)
Learning activities
Teaching activities
(Learners are expected to:)
Activity 1
Demonstrate to learners how to use the conditions for similar
triangles to prove that triangles are similar.
1. Study the figure below and answer the questions that follow.
follow demonstration and
engage in questions as
demonstration unfolds.
copy example in their
notebooks.
B
A
Q
P
C
(a) Prove that ∆ ABC /// ∆ PQC
(b) Calculate the length of AB
If AC = 10 units
PC = 4 units
PQ = 2 units
Solution
Statement
(a) In Δ ABC and Δ PQC:
̂
𝐶 is common
𝐴𝐵̂𝐶 = 𝑃𝐴̂𝐶
𝐵𝐴̂𝑃 = 𝐴𝑃̂𝐶
∴ Δ ABC /// Δ PQC
Reason
Corresponding ∠s (AB // EC)
Corresponding ∠s (AB // EC) or
Sum of interior angles of ∆
(A,A,A)
(b) In Δ ABC and Δ PQC:
𝐴𝐵 𝐵𝐶 𝐴𝐶
=
=
𝑃𝑄 𝑄𝐶 𝑃𝐶
Δ ABC /// Δ PQC
𝐴𝐵 10
=
2
4
4 𝐴𝐵 = 20
𝐴𝐵 = 5
Grade 9 Lesson Plan: 1+4 Intervention – Term 2
(Draft)
Page 3 of 5
Activity 2
Work through the problem showing learners how to use the
properties of similar triangles to find unknown sides
Calculate the length of the unknown sides if ∆ABC /// ∆ PTS
A
12𝑐𝑚
𝑥
P
S
45°
45°
6𝑐𝑚
C
2𝑐𝑚
76°
76°
3𝑐𝑚
B
T
Possible solution
𝐴𝐵
𝑃𝑇
6
2
𝐵𝐶
=
=
𝑇𝑆
12
6𝑥 = 24
6
=
𝐴𝐶
𝑃𝑆
(Given ∆ABC /// ∆ PTS)
Substitute the given sides
𝑥
6 12
=
2
𝑥
6𝑥
=
24
Cross multiply
Applying the multiplicative
inverse
6
𝑥=4
Grade 9 Lesson Plan: 1+4 Intervention – Term 2
(Draft)
Page 4 of 5
8. CLASSWORK (Suggested time: 15 minutes)
̂ = 50° and R
̂ = 60°. In ∆ TSM, TM =4,8 cm, SM = 4,5 cm,
1. In ∆ PQR, PQ =7,5 cm, QR = 6,4 cm, P
̂S = 70° and T
̂ = 60°.
̂ with reasons.
a) Write down the size of M
b) Prove that ∆ PQR /// ∆ MST.
c) Calculate the lengths of PR and ST.
9. CONSOLIDATION/CONCLUSION & HOMEWORK (Suggested time: 5 minutes)
a) Homework
1. Study the figure below and answer the following questions:
(a) Prove ∆PQM /// ∆ SRM.
(b) Calculates the lengths of PM and PQ.
P
Q
72 mm
M
56 mm
R
42 mm
70 mm
SS
2. Consider the similar triangles drawn below using concentric circles. Explain why the triangles are
similar in each diagram.
G
H
I
K
J
V
U W Y
F
Grade 9 Lesson Plan: 1+4 Intervention – Term 2
(Draft)
Z
X
A
Page 5 of 5