Illustrating Triangle Congruence

1. “RESPECT FOR OURSELVES
GUIDES OUR MORALS,
RESPECT FOR OTHERS GUIDES
OUR MANNERS”
-Lawrence Sterne

2. MOTIVATIONAL
ACTIVITY

3. PREPARED BY: JESSA M. MAGAN
TRIANGLE CONGRUENCE

4. LESSON OUTCOMES
At the end of the lesson, students can:
• define what is triangle congruence;
• discuss the parts of a triangle;
• illustrate the properties of triangle congruence;
• identify the corresponding angles and sides of the triangle; and
• apply the idea of congruence in real-life situations.

5. WHAT IS TRIANGLE CONGRUENCE?
A triangle has
three sides, three
vertices and three
angles.
TRIANGLE CONGRUENCE
It means having the
same shape and
size, and denoted by
≅.

6. WHAT IS TRIANGLE CONGRUENCE?
 Two triangles are congruent if and
only if their corresponding parts
(sides and angles) are congruent.

7. PARTS OF A TRIANGLE
A
B C
VERTICES: A, B, C
SIDES: AB, BC, AC
ANGLES: A, B, C

8. EXAMINE THE FIGURES!

9. PROPERTIES OF TRIANGLE CONGRUENCE
Reflexive Property
Δ𝑋𝑌𝑍 ≅ ΔXYZ
Symmetric Property
If Δ𝑋𝑌𝑍 ≅ ΔQRS, then ΔQRS ≅ Δ𝑋𝑌𝑍.
Transitive Property
If Δ𝑋𝑌𝑍 ≅ ΔQRS and ΔQRS ≅ ΔMNO, then
ΔXYZ ≅ Δ𝑀𝑁𝑂

10. CORRESPONDENCE
The symbol for ‘correspondence’ is
AB DE Can be read as the “line segment AB corresponds
to line segment DE”.
A B
Can be read as the “angle A corresponds to angle
B”.

11. By definition: Two triangles are congruent if and only if their
corresponding parts (sides and angles) are congruent.
Corresponding parts of congruent triangles are congruent
(CPCTC).
A
B C
F
D
E
𝜟𝑨𝑩𝑪 ≅ 𝚫𝐃𝐄𝐅

12. EXAMPLE
A
B
C F
D
E
𝜟𝑨𝑩𝑪 ≅ 𝚫𝐃𝐄𝐅
CORRESPONDING ANGLES
A D
B E
C F
CORRESPONDING SIDES
AB DE
BC EF
AC DF

13. LET’S TRY!
C
A
T G
D
O
𝜟𝑪𝑨𝑻 ≅ 𝚫𝑫𝑶𝑮
CORRESPONDING ANGLES
C D
A O
T G
CORRESPONDING SIDES
CA DO
AT OG
TC GD

14. TRY THIS!
Direction: Identify corresponding angles and corresponding sides that will prove that the two
triangles are congruent.
B
A
T W
C
O
𝜟𝑩𝑨𝑻 ≅ 𝚫𝑪𝑶𝑾

15. ANSWER KEY
BA CO or
AT OW or
CORRESPONDING ANGLES
B C or
A O or
T W or
CORRESPONDING SIDES
TB WC or
AB OC
TA WO
C B
O A
W T
BT W C

16. Individual Task:
Given 𝜟MAN ≅ 𝜟DEN. Name the corresponding part of each of the
following:
1. M 6. E
2. END 7. MAN
3. D 8. AN
4. MN 9. ND
5. NE 10.DN

17. M
N
A E
D
N
𝜟𝑴𝑨𝑵 ≅ 𝚫𝑫𝑬𝑵

18. ANSWER KEY
1. M D 6. E A
2. END ANM 7. MAN DEN
3. D M 8. AN EN
4. MN DN 9. ND NM
5. NE NA 10.DN MN

19. GET ½ CROSSWISE!
½ CROSSWISE MA’AM?
YES PO, ½
CROSSWISE.

20. TRIANGLE SUM THEOREM
C
A
T
• The sum of three interior angles in a triangle is always 180˚.
90˚ 30˚
x
C+ A+ T = 180˚
X+90˚+30˚= 180˚
X+120˚= 180˚
X= 180˚- 120˚
X= 60˚

21. FIND THE LENGTH OF THE SIDES
C
A T G
D
O
𝜟𝑪𝑨𝑻 ≅ 𝚫𝑫𝑶𝑮
7m
5m
10m

22. THANK YOU FOR
LISTENING!