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Semi-Detailed Lesson Plan
Mathematics VIII
Content Standard:
The learners will demonstrate understanding of key concepts of
axiomatic structure of geometry and triangle congruence.
Performance Standard:
The learners are able to communicate mathematical thinking with
coherence and clarity in formulating, investigating, analyzing, and solving
real-life problems involving congruent triangles using appropriate and
accurate representations.
Learning Competency:
The learners will illustrate triangle congruence.
I – Objective
At the end of the lesson, 83% of the students will be able to:
- define triangle congruence;
- identify corresponding parts of congruent triangles.; and
- apply the concept of triangle congruence to solve problems.
II – Subject Matter
Topic : Illustrating triangle congruence
References : Wow Math, Mathematics Quarter 3 Self-Learning Modules pp
Instructional Materials : Visual Aids, chalk, eraser
III – Learning Procedure
A. Preparation
Prayer
Greetings
Checking of Attendance
Classroom Management
Review
Illustrating Axiomatic Structure of a Mathematical
System
Briefly review the previous lesson on illustrating axiomatic
structure of a mathematical system.
B. Lesson Proper
A. ACTIVITY: “CUT ME AND COMPARE”
Description: Divide the class into small groups. Give each
group construction paper, scissors, and rulers. Instruct them
to cut out two triangles that they think are congruent. Then,
have them compare their creations with other groups to see if
they were successful.
Directions: Cut out two triangles by group and compare to
the other group.
B. ANALYSIS
What have you observed upon taking the activity?
Was the activity easy? Did you face any challenges
while dealing with the activity? If so, what are those?
C. ABSTRACTION
Congruence- Means having the same shape and size, and it
is denoted by ≅. The top part of the symbol, ~ , is the sign for
similarity and indicates the same shape. The bottom part symbol,
= , is the sign of equality and indicates the same size
Correspondence- Pairing the parts of one group to the parts
of another group is called correspondence. Correspondence uses
the notation “
Examples:
A E
N T G O
Assume ∆ NAT coincide with ∆ GEO , such that the vertices of
∆ NAT fit exactly over the vertices of ∆ GEO. The correspondence can be
created between triangles.
∆ NAT ↔ ∆ GEO
- In triangles ABC and DEF, side AB is congruent to side DE, angle A is
congruent to angle D, and side AC is congruent to side DF. Which
criterion proves the two triangles are congruent?
o a) SSS
o b) SAS
o c) ASA
o d) None of the above
- Which of the following sets of side lengths can NOT form a triangle?
o a) 3 cm, 4 cm, 5 cm
o b) 2 cm, 6 cm, 8 cm
o c) 7 cm, 3 cm, 10 cm
o d) 10 cm, 4 cm, 7 cm
- Two triangles are congruent if they have:
o a) two congruent sides and one congruent angle.
o b) three congruent angles.
o c) two congruent angles and one congruent side opposite to
them.
o d) all corresponding sides and angles congruent.
Test 2
Instructions: Fill in the blanks the correct correspondence.
1. H Y
I J X Z
Corresponding
Vertices
Corresponding Angles Corresponding Sides
H ↔ ___
___ ↔ X
___ ↔ Z
¿ H ↔ ___
¿ I ↔ ___
¿ J ↔ ___
HI ↔ ___
___ ↔ YZ
IJ ↔ ___
2. R E
O W B T
Corresponding
Vertices
Corresponding Angles Corresponding Sides
R ↔ ___
___ ↔ B
___ ↔ T
¿ R ↔ ___
¿ O ↔ ___
¿ W ↔ ___
RO ↔ ___
___ ↔ ET
OW ↔ ___
Test 3
Instructions: Solve the following problem and show your work.
A rectangular garden bed needs to be divided into two
congruent triangular sections. The length of the garden bed is 12
meters, and the width is 5 meters. What are the side lengths of each
triangular section? Explain how you arrived at your answer.
V – Assignment
Answer the following questions on triangle congruence on a
plain sheet of paper.
Instructions: Solve the following problems involving triangle congruence.
- In triangle ABC, side AB is 8 cm longer than side AC, and side BC is 3
cm shorter than side AC. If the perimeter of triangle ABC is 30 cm,
find the lengths of all three sides.
- Two isosceles triangles, XYZ and PQR, have a congruent vertex
angle (∠Y ≅ ∠P) and a congruent base angle (∠X ≅ ∠Q). Prove that
triangles XYZ and PQR are congruent.
- A rectangular piece of cardboard needs to be cut into two congruent
right triangles. The length of the cardboard is 20 cm, and the width
is 12 cm. What are the side lengths of each right triangle after
cutting?
Prepared by: Checked by:
Lea Angela A. Llorente Mr. Marcel Orge
Pre-Service Teacher Cooperating
Teacher
