PowerPoint for Illustrating Triangle Congruence; used during COT

2. E R T E X
V

3. S I D E

4. A N G L E

5. T R I A N G L E

6. C O N G R U E N T

7. Based on the words
depicted in the game we
had, what could be our
possible lesson for today?

8. ILLUSTRATING
TRIANGLE
CONGRUENCE

9. Objectives:
1. Define and illustrate triangle
congruence.
(M8GE-IIId-1)
2. Identify corresponding
parts of two congruent
triangles.
3. Relate triangle congruence
in real-life.

10. Activity: TANGRAM PIECES
Direction: Place the numbered
tangram pieces to complete the
puzzle.

18. 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.

19. IDEA OF CONGRUENCE
The idea of congruence always
helps to recognize congruent
figure in the same orientation.
When two figures are congruent,
you may slide, flip, or rotate the
figures until they overlap
exactly.

20. IDEA OF CONGRUENCE
Bills and Coins
Keys
Spoons

21. How can we say that two
triangles are congruent?

22. PARTS OF A TRIANGLE
In geometry, a triangle is a
closed, two-dimensional shape
with three straight sides. It is a
polygon.
A triangle has three sides, three
vertices and three angles.

23. PARTS OF A TRIANGLE
A
C
B
Sides: 𝐴𝐵, 𝐵𝐶, 𝐴𝐶
Angles: ∠𝐴, ∠𝐵, ∠𝐶
Vertices: 𝐴, 𝐵, 𝐶

24. CORRESPONDENCE
Pairing the parts of one group to
the parts of another group is
called correspondence.
Correspondence uses the
notation “↔”.

25. CORRESPONDENCE

26. CORRESPONDENCE
In this correspondence, there are three pairs of
corresponding vertices, angles, and sides.

27. CORRESPONDENCE
Conclusion: Since the vertices of
∆NAT fit exactly with the vertices
of ∆GEO, therefore ∆NAT and
∆GEO are congruent. In symbols,
∆NAT≅∆GEO
(Read as “triangle NAT is congruent
to triangle GEO”)

28. CORRESPONDENCE
Note: In naming congruent triangles,
the order of the letters representing
the vertices of one triangle shall be
written in the same order as their
corresponding vertices in the other
triangle.

29. CONGRUENT TRIANGLES
Two triangles are congruent if and only
if their corresponding parts (sides and
angles) are congruent.
This definition is abbreviated as CPCTC,
which means Corresponding Parts of
Congruent Triangles are Congruent.

30. CONGRUENT TRIANGLES

31. Answer the following:
1. ∆CAT≅∆DOG. Write down the pairs of
corresponding parts.

32. 2. Given that the two triangles below are
congruent, list the pairs of congruent angles and
congruent sides and then name the congruent
triangles.

33. REAL-LIFE APPLICATION OF CONGRUENT
TRIANGLES
View from the Giza Plateau of the three pyramids known as Queens'
Pyramids with three smaller three satellite pyramids in front. In order from
left to right: the Pyramid of Menkaure, Khafre and then Khufu.

34. REAL-LIFE APPLICATION OF CONGRUENT
TRIANGLES
FUN FACT: To get to the top of the Eiffel tower, you’ll have to climb
1,665 steps.
Eiffel Tower

35. REAL-LIFE APPLICATION OF CONGRUENT
TRIANGLES
FUN FACT: The Ferris Wheel was Invented in 1893 for the Chicago
World's Fair. The inventor George W. Ferris was a bridge builder.
MOA’s Ferris Wheel

36. REAL-LIFE APPLICATION OF CONGRUENT
TRIANGLES
Magsaysay Bridge is named after the 7th president of the Philippines,
Ramon Magsaysay. It is an arched-type steel bridge built during the early
sixties that spans the mighty Agusan River.
Magsaysay Bridge at
Butuan City

37. EVALUATION:

39. PERFORMANCE TASK NO. 3
TANGRAM PUZZLE
Directions: A Tangram puzzle focuses on the
objective of rearranging the seven separate
pieces into a complete image of various shapes (in
outline or silhouette only). Create four (4)
tangram puzzles by following the steps below.

40. PERFORMANCE TASK NO. 3
Materials needed:
• Ruler
• Pencil
• Felt-tip pen or ballpen
• Eraser
• Construction paper/colored paper/any thick
paper
• Scissors
• Glue

41. STEP 1
Draw a 4-inch square with your pencil on any
thick paper.

42. STEP 2
You need to draw a grid of smaller squares
onto your current square.
So, get your pencil out and draw a 1-inch grid
in the 4-inch square.
1 inch

43. STEP 3
You now need to draw the lines that will mark
out the edges of each tangram piece. These
should be drawn darker than your grid lines.
With the felt-tip pen, draw your first line
from the bottom left corner to the top right
corner, effectively creating two large
triangles.

44. STEP 3

45. STEP 4
Create another triangle in the top left corner.
Start from halfway down your main piece on
the left side and draw a diagonal line that
meets the top of your square in the middle.

46. STEP 4

47. STEP 5
Draw a diagonal line from the bottom right
corner of the grid through the center of your
first line and stop at your second line.

48. STEP 6
Your fourth line will join your first and second
line together. Draw a diagonal line from the
point where your second line intersected the
top edge. Draw through one square to the
point where it meets your first line. It should
meet the line at the bottom right corner of
the grid square. You should be able to see
that you have drawn four clearly defined
triangles and one square.

49. STEP 6

50. STEP 7
Your last line should be drawn from the point
where your second and third lines meet (also
the middle of your second line). Draw the line
downwards on your grid until it meets your
first drawn line. Now your tangram set is
completed, you should see 5 clearly defined
triangles, a square and a parallelogram.

51. STEP 7

52. STEP 8
Rub out your lightly marked grid.

53. STEP 9
Cut out the pieces. There are seven pieces.

54. STEP 10
Rearrange the seven pieces into this image.

55. STEP 11
Paste your output on a long bond paper.

56. STEP 12
Repeat Steps 1 to 9 to create 3 more puzzles.
And arrange them into the following:

57. STEP 12
For the
fourth
puzzle,
create your
image and
name what it
is.