This document discusses geometry concepts like congruence, triangles, and their properties. It contains examples of: - Using tangram pieces to complete a puzzle based on congruent shapes - How congruence is used in mass production by ensuring identical copies are made - Properties of triangle congruence like the reflexive, symmetric, and transitive properties - Identifying sides, angles, and vertices of triangles in examples - Defining terms and listing properties of congruence The document provides instruction and activities to help students learn about geometric concepts like congruence through examples, definitions, and identifying parts of shapes.

2. Review
What are the undefined terms of
geometry?
Point Line Plane
X Y
X

3. OBJECTIVES
AT THE END OF THE LESSON THE STUDENTS
SHOULD BE ABLE TO;
discuss the idea of congruence
use the properties of congruence in identifying
congruent parts and congruent triangles; and
identifies triangle parts

5. Instruction: Place the numbered tangram pieces to
complete the puzzle.
2
1
3
5
4
6

6. What is the main idea of this activity?
•The player searches
for the tangram
piece that is exactly
similar to the space
on the board, or that
is congruent to it.
1
2
5
6
4

7. How did you solve the puzzle?
How did congruency affect you in solving the
puzzle?

8. Congruence means having same
shape and size, and it is denoted
by ≅ . The top part symbol is the
sign for similarity and indicates
the same shape. The bottom part
symbol is the sign of equality
and indicates same size.

9. Idea of congruence
Can you see how the idea of congruence is used in
the mass production of various products?
The idea of congruence always helps to recognize
congruent figures in the same orientation. When
two figures are congruent, you may slide, flip, or
rotate the figures until they overlap exactly.

10. Properties of triangle congruence
The properties of equality as well as the properties
of congruence that follow from them are often used
in doing formal geometric proof.
Reflexive property of
congruence
Symmetric property
of congruence
Transitive property
of congruence
AB≅AB
∠A≅∠A
If AB ≅ CD, then CD ≅ AB
If ∠A ≅ ∠B , then ∠B ≅ ∠A
If AB ≅ CD and CD ≅ EF,
then AB ≅ EF
If ∠A ≅ ∠B and ∠B ≅ ∠C,
then ∠A ≅ ∠C

11. Group activity
Identify the properties and definitions of terms that
can justify each of the following statements based
on the given facts.
Given: B is the midpoint of segment AC.
BC≅CD

12. Given: B is the midpoint of segment AC.
BC≅CD
STATEMENTS REASONS
AB ≅ BC DEFINITION OF MIDPOINT
Group 1 AB ≅ AB
Group 2 CD ≅ BC
Group 3 AB ≅ CD
A D
C
B
Transitive property of congruence
Symmetric property of congruence
Reflexive property of congruence

13. TRIANGLE
In geometry, a triangle is closed, two – dimensional shape
with three straight sides. It is also a polygon.
A triangle has three sides, three vertices and three angles
C
B
A
ABC
Sides: AB, AC, BC
Angles: ∠A, ∠B, ∠C
Vertices: A, B , C

14. GROUP ACTIVITY
Instruction: Identify the side, angles, vertices and
name the triangle.

15. Instruction: Identify the side, angles,
vertices, and name the triangle.
Group 3
Group 1 Group 2
H
J
I Y Z F G
X E

16. ½ sheet of paper
A. Instruction: List all the angles,
vertices, and sides of the following
triangles:
K
N
L M
O
Q
P
R
S

17. B. Instruction: define the following terms.
1. Reflexive property of congruence
2. Symmetric property of congruence
3. Transitive property of congruence

18. Assignment
In your notebook write the definition of
postulates and theorems. Give an
example at least 5.