mathematics

2. ACTIVITY 1:
TANGRAM PUZZLE

3. Re-arrange the following shapes
to form a TRIANGLE.

7. Can you cite things that are congruent
with each other?
PAPER BILLS CD TAPES ORIGINAL
AND
DUPLICATE
KEY

9. Parts of a
Triangle
Triangle
- Closed plane
figure with three
sides and three
angles
- It is also a
polygon Three sides
Three vertices
Three angles
∆ ABC

10. CLASSIFICATION OF TRIANGLES ACCORDING TO
SIDES
EQUILATERAL
TRIANGLE
3 congruent sides
ISOSCELES
TRIANGLE
at least 2
congruent sides
SCALENE
TRIANGLE
no congruent sides

11. CLASSIFICATION OF TRIANGLES ACCORDING TO
ANGLES
EQUIANGULAR
TRIANGLE
3 congruent
ANGLES
ACUTE
TRIANGLE
3 acute
ANGLES
RIGHT
TRIANGLE
1 right ANGLE
OBTUSE TRIANGLE
1 obtuse ANGLE

12. ARE WE
CONGRUENT?
Yes, we are!

13. ARE WE
CONGRUENT?
No, we are not

14. Which of these shapes is congruent with the
first shape?
Even though their direction changed, they are
the same in size and shape.

15. CONGRUENT
In Geometry, two figures are congruent if they
have the same shape and size.
≅ - symbol of congruent
~ - similar in shape
= - same size

16. Idea of CONGRUENCE
When two figures are
congruent, you may slide,
flip or rotate the figures
until they overlap exactly.

17. AB = CD
𝑨𝑩 ≅ 𝑪𝑫
2.5 cm = 2.5 cm
𝑨𝑩 ≅ 𝑩𝑪
𝑬𝑫 ≅ 𝑭𝑮
𝑬𝑭 ≅ 𝑫𝑮

18. Properties of Triangle
Congruence
Reflexive
Property
of
Congruenc
e
Symmetric
Property
of
Congruenc
e
𝑨𝑩 ≅ 𝑨𝑩
∠𝑨 ≅ ∠A
𝑨𝑩 ≅ 𝑪𝑫
𝑪𝑫 ≅ 𝑨𝑩
∠𝑨 ≅ ∠B
∠𝑩 ≅ ∠A

19. Properties of Triangle
Congruence
Transitiv
e
Property
of
Congruenc
e
𝑨𝑩 ≅ 𝑪𝑫 ∠𝑨 ≅ ∠B
𝑪𝑫 ≅ 𝑬𝑭
𝑨𝑩 ≅ 𝑬𝑭
∠𝑩 ≅ ∠C
∠𝑨 ≅ ∠C

20. CORRESPONDENCE
The symbol for
“correspondence to” is
↔
𝑨𝑩 ↔ 𝑫𝑬
is read as “line segment AB
corresponds to line segment
DE

21. Two triangles are congruent if
and only if all their
corresponding parts are
congruent.
Corresponding Parts of Congruent
Triangles are Congruent (CPCTC)

22. A
B C
E
F
D

23. A
B C
E F
D

24. A
B C
E
F
D
∆ ABC ≅ ∆ DEF

25. A
B
C
E F
D
Corresponding
Angles
Corresponding
Sides
∠𝑨 ↔ ∠D
∠𝑩 ↔ ∠E
∠𝑪 ↔ ∠F
𝑨𝑩 ↔ 𝑫𝑬
𝑩𝑪 ↔ 𝑬𝑭
𝑨𝑪 ↔ 𝑫𝑭
Congruence
Statement
∆ ABC ≅ ∆
DEF
∆ ABC ≅ ∆
EDF

26. Show that the two triangles are
congruent.
C
A
T
O G
D
Corresponding
Angles
Corresponding
Sides
∠𝑪 ↔ ∠D
∠𝑨 ↔ ∠O
∠𝑻 ↔ ∠G
𝑪𝑨 ↔ 𝑫𝑶
𝑨𝑻 ↔ 𝑶𝑮
𝑪𝑻 ↔ 𝑫𝑮
∆𝐂𝐀𝐓 ≅ ∆DOG

27. Which pairs of figures are congruent
by inspection?

31. ANGLES SIDES

32. ANGLES SIDES

33. Corresponding
Angles
Corresponding
Sides
Congruence Statement:

36. TRIANGLE SUM THEOREM
The sum of the three interior angles
in a triangle is always 180º
A
B C
∠𝑨 + ∠B + ∠C = 180º ∠𝑨 = 65º

37. A
B C
Included side of ∠𝑨
and ∠B
𝑨𝑩
Included side of ∠B
and ∠C
𝑩𝑪
Included side of ∠A
and ∠C
𝑨𝑪
Included angle of 𝑨𝑩
and 𝑩𝑪
∠B
Included angle of 𝑨𝑪
and 𝑪𝑩
∠C
Included angle of 𝑩𝑨
and 𝑨𝑪
∠A

38. A
B C
Opposite side of ∠𝑨 𝑩𝑪
Opposite side of
∠B
𝑨𝑪
Opposite side of
∠C
𝑨𝑩
Opposite angle of 𝑨𝑩 ∠C
Opposite angle of 𝑨𝑪 ∠B
Opposite angle of 𝑩𝑪 ∠A

40. TRIANGLE
CONGRUENCE
POSTULATE

41. TRIANGLE CONGRUENCE POSTULATE