The document discusses the fundamental concepts of geometry, including definitions of points, lines, planes, and polygons. It categorizes polygons into convex and concave types, explains the classification of polygons based on congruency, and describes how to name polygons. Additionally, it includes interactive activities related to identifying and naming polygons.

1. Measurement and
Geometry
First Quarter, S.Y. 2024-2025

2. Geometry

7. GEOMETRY
Geometry is one of the classical
disciplines of math.
The word geometry was derived from
two Greek words, geo and metron,
which mean earth and measure,
respectively

8. Point
Line
Plane
U N D E F I N E D T E R M S

9. U N D E F I N E D T E R M S :
1. Point

10. U N D E F I N E D T E R M S :
1. Point ∠

11. U N D E F I N E D T E R M S :
1. Point

12. U N D E F I N E D T E R M S :
1. Point ?
?
?
? ?
?
?
?
?

13. U N D E F I N E D T E R M S :
1. Point
A
B
C
D
F
G
E
H
I
Point A

14. U N D E F I N E D T E R M S :
2. Line

15. U N D E F I N E D T E R M S :
A
B
2. Line
m
Line AB
Line m
´
𝐴𝐵

16. U N D E F I N E D T E R M S :
3. Plane

17. U N D E F I N E D T E R M S :
A
B
C

18. U N D E F I N E D T E R M S :
A
B
C
3. Plane

19. U N D E F I N E D T E R M S :
A
B
C
3. Plane

20. is primarily developed
to be a practical guide
for measuring lengths,
areas, and volumes, and
is still in use up to now.
GEOMETRY

27. Pictures will be displayed, and
players have 5 seconds to write
down the polygon’s name based on
the number of sides and what
polygon it reminds them. Correct
answer earns 1 point.

29. Triangle

31. Quadrilateral

33. Pentagon

35. Quadrilateral

37. Octagon

39. The name of a polygon will be flashed
on the screen and, the players have 5
seconds to write down the number of
sides. The correct answer earns 1 point.

40. Triangle

42. Quadrilateral

44. Pentagon

46. Octagon

48. What is a
polygon?

50. Which figure is a
polygon?

51. Polygons
The figures below are polygons. They are closed, plane figures,
made of line segments, and the segments intersect only at their
endpoints.

52. These are not polygons
Not a plane
figure
Sides do not
intersect at their
endpoints

53. What is a
polygon?

54. Polygon
is a closed-plane
figure bounded by
line segments that
meet only at their
endpoints.

56. Classification of Polygons
Polygons could be classified either as convex or concave. A polygon is
convex if no diagonal is in the exterior of the polygon. A polygon is
concave if at least one diagonal is in the exterior of the polygon.
A polygon consists of segments for its sides. If you extend each of the
segments past its endpoints and none of these resulting lines pass through
the inside or interior of the polygon, then the polygon is convex. Otherwise,
if even one extended side cuts into the interior of the polygon, then the
polygon is concave.

58. Types of Polygons
The different types of polygons in
terms of congruency of parts are
equilateral, equiangular, and
regular. A polygon is equilateral if
all its sides are equal;
equiangular if all its angles are
equal; regular if both sides and
angles are all equal.

62. How do we name
polygons?

64. Naming a Polygon

65. Polygons are named by writing their consecutive vertices in order,
such as ABCDE or AEDCB or CDEAB or CBAED for the figure on the left.
A polygon separates a plane into three sets of points: the polygon itself,
points in the interior of the polygon, and points in the exterior of the
polygon.
The parts of a polygon are the sides, vertices, interior and exterior angles,
and diagonals. An exterior angle of a polygon is an angle that is both
supplement and adjacent to one of its interior angles.

67. - Consecutive vertices are vertices on the same side of the polygon.
- Consecutive sides are sides that have a common vertex.
- A diagonal is a segment joining non-consecutive vertices.
A polygon separates a plane into three sets of points: the polygon itself,
points in the interior of the polygon, and points in the exterior of the
polygon.

68. DIY: Name the polygon.
Name:
Diagonals:
Angles:
Vertices:
Sides:

70. What do you know about a square?

71. No. of
Sides
No. of
diagonals
from a
fixed
vertex
No. of
triangles
formed
Sum of the
interior angles
Measure of
each interior
angle of a
regular polygon
3
4
5
6
7
8
9
10
n

77. Example. Compute for the sum of interior angles of a convex decagon.