SAS

1. PRAYER

2. ENERGIZER
Brain Teaser
What can be swallowed, but can also
swallow you?
PRIDE
Until I am measured, I am not known.
Yet you miss me, when I have flown.
What am I?
Time

5. Corresponding
Vertices
Congruent Sides Congruent Angles

6. Corresponding
Vertices
Congruent
Sides
Congruent
Angles

9. ∠ABC or ∠ B
INCLUDED PART

10. 𝐸𝐹
INCLUDED PART

11. INCLUDED PART

12. ∆ABC≅ ∆𝑃𝑄𝑅
SAS Congruence
Postulates
𝑆𝐼𝐷𝐸-ANGLE-SIDE
𝐴𝐵 ≅ 𝑃𝑄
∠ABC≅ ∠𝑃𝑄𝑅
CONGRUENT
PARTS
SIDE
ANGLE
SIDE 𝐵𝐶 ≅ 𝑄𝑅

13. ∆ABC≅ ∆DEF
ASA Congruence
Postulates
ANGLE-SIDE -𝐴𝑁𝐺𝐿𝐸
∠ABC≅ ∠𝐷𝐸𝐹
CONGRUENT
PARTS
SIDE
ANGLE
ANGLE
𝐵𝐶 ≅ 𝐸𝐹
∠BCA ≅ ∠𝐸𝐹𝐷

14. ∆ACB≅ ∆PRQ
SSS Congruence
Postulates
SIDE-SIDE -𝑆𝐼𝐷𝐸
CONGRUENT
PARTS
SIDE
SIDE
SIDE
𝐴𝐶 ≅ 𝑃𝑅
𝐶𝐵 ≅ 𝑅𝑄
𝐵𝐴 ≅ 𝑄𝑃

15. Direction: Determine the congruent parts using the
figure below and tell whether if it is ASA, SAS, and
SSS Congruence Postulates
ASA Congruence
Postulates
TRY IT!!
ANGLE SIDE ANGLE
TRY IT!!

16. TRY IT!!
SIDE ANGLE
2.
SIDE
SAS Congruence
Postulates

17. SIDE SIDE
3.
SIDE
TRY IT!!
SSS Congruence
Postulates

18. PROVING
CONGRUENCE OF
TRIANGLES

19. THEOREMS

20. Objectives
• The learner should be able to:
• 1. Illustrates Triangle Congruence using
• a. Congruence postulates
• b. Theorems
• 2. Prove deductively the Congruence of two
triangles.
• 3. Developed willingness and interest in proving
triangle congruence.
• 4. Appreciate the concept of logical ideas to
their peers.

21. (AAS) Angle
Angle Side
DISCUSSION
1
.

22. (AAS) Angle
Angle Side
(if in two triangles, two angles and non included sides
of one triangle are congruent to the corresponding
two angles and non included sides of another triangle,
then the triangles are congruent)
DISCUSSION
1
.

23. It is Hypotenuse
Acute Angle
DISCUSSION
2
.
HyA
Theorem
Hypotenuse
Acute Angle

24. DISCUSSION
2
.
The two triangles are congruent if the Hypotenuse
and acute angle of one triangle are Congruent to the
Hypotenuse and acute angle of another triangle.
HyA
Theorem

25. If a leg and the hypotenuse of a right triangle are
congruent to corresponding parts of another right
triangle, then the two triangles are congruent
DISCUSSION
3
.
HyL
Hypotenuse
Legs

26. DISCUSSION
4
.
LA THEOREM
Legs
Acute Angle

27. The leg and an acute angle of a right
triangle are congruent then the two
triangles are congruent
DISCUSSION
4
.
LA THEOREM

28. If the legs of one right triangle are
correspondingly congruent to the legs of
another triangle, then the two triangles are
congruent.
DISCUSSION
5
.
LEG LEG
THEOREM

29. STEP 1. Identify what the given are,
and what is to be proved. Mark gives
the given information on the diagram
STEP 2. Identify the congruence
theorem to be used and the
additional information needed and
why.
DISCUSSION

30. ACTIVITY 1.2
Direction: Complete the two column proof
below by supplying the correct statement and
reason.
DISCUSSION

31. STATEMENTS REASON
1.Given
3.Definition of
Angle Bisector
2. Given
DISCUSSION
PROOF

32. STATEMENTS REASON
4. Reflexive Property
5. AAS Congruence
Theorem
DISCUSSION
PROOF

33. A. What are the different
CongruenceTheorems?
AAS Congruence Theorem
if in two triangles, two angles and
non included sides of one triangle are
congruent to the corresponding two
angles and non included sides of
another triangle, then the triangles
are congruent
ABSTRACTION

34. If the hypotenuse and an acute
angle of a right triangle are congruent
to the corresponding parts of another
right triangle, then the two triangles
are congruent.
ABSTRACTION
HyA Congruence Theorem

35. HyL Congruence Theorem
If a leg and the hypotenuse of a right
triangle are congruent to
corresponding parts of another right
triangle, then the two triangles are
congruent
ABSTRACTION

36. LA Theorem
• The leg and an acute angle of a right
triangle are congruent then the two
triangles are congruent.
LL Theorem
If the legs of a right triangle are
congruent to the corresponding parts of
another right triangle, then the two
triangles are congruent.
ABSTRACTION

37. B. How about the different steps in
writing two columns proof?
Identify what the given are, and
what is to be proved. Mark gives
the given information on the
diagram
ABSTRACTION

38. B. How about the different steps in
writing two columns proof?
Identify the congruence theorem to
be used and the additional
information needed and why.
ABSTRACTION

39. APPLICATION
TEST YOURSELF
A. Directions: Give the congruence
statement for each pair of triangles
and name the theorems that justify
congruence.

40. Hypotenuse Leg
Theorem
APPLICATION
1
.

41. Angle Angle Side Theorem
APPLICATION
2
.

42. B. Prove Me!
Directions: Write the missing
statements and reasons to complete
the logical proof of stated problem.
APPLICATION

43. APPLICATION

44. STATEMENTS REASONS
1.Given
3.Given
2.Definition of Midpoint
APPLICATION
PROOF:

45. STATEMENTS REASONS
4.Definition of
Perpendicular lines
5. Definition of Right
Triangles
6.LL Theorem
APPLICATION
PROOF:

46. PERFORMANCE
TASK

47. I. In each figure, congruent parts are marked. Give
additional parts to prove that the triangles are
congruent and name the postulates or theorem that
justifies the congruence.
EVALUATION
A
.

48. Guided Questions:
1. How did you identify the theorems?
2. How did you identify the additional
part to prove that the two triangles
are congruent?
EVALUATION

49. 3. Were you able to give additional
congruent part to prove that the
two triangles are congruent? If
yes, how?

50. EVALUATION
B
.

51. EVALUATION

52. Guided Questions:
1. How did you identify the theorems?
2. How did you identify the additional
part to prove that the two triangles
are congruent?
EVALUATION

53. 3. Were you able to give additional
congruent part to prove that the
two triangles are congruent? If
yes, how?

55. 2
Mrs. Romana P. Bacsa
THANK YOU !!
GOD BLESS
EVERYONE
KEEP SAFE!!