Geometry is the branch of mathematics that measures and compares points, lines, angles, surfaces, and solids. It defines basic shapes such as points, lines, rays, angles, and planes. It also covers types of angles and intersections between lines. Additionally, it categorizes polygons by number of sides and characteristics. Key concepts include perimeter, area, symmetry, and three-dimensional solids. The document provides definitions and examples of basic geometric elements, shapes, their properties, and how to measure them.

3. Geometry: a branch of mathematics that
measures and compares
.
points, lines, angles, surfaces, and solids

4. What are:
Points?
Lines?
Angles?
Surfaces?
Solids?

5. The Basics

6. Point:
a single, exact location in space
A point is represented with dot
and label with a letter.
This is how we represent Point A
A .

7. Line:
A straight path that is made of
endless points in both directions
A line is represented by connecting two
labeled points with an arrow on each end.
Add a second labeled point (B)
A
. .
B
This is how we represent Line AB

8. Line Segment:
Part of a line that extends from
one point to another point
A line segment is represented by
connecting two labeled points
A
. .
B
This is how we represent Line AB

9. Parallel lines or line segments:
A pair of lines on the same plane that are the
same exact distance apart and never intersect
(meet)
A___________________B
C___________________D
Line segment AB and line segment CD are the
same distance apart. They will never intersect

10. Ray:
Part of a line, having only one point
A
This is ray A, written as A

11. Angles

12. Angle:
Two rays that have the same
point of origin or vertex
Ray AB and ray AC form angle BAC
C
A B

13. Angle:
There are three types of angles,
Acute, Obtuse, and Right angles.
Acute angles
Measure: between
0 and 89 degrees
Obtuse angles
Measure: between 91
And 179 degrees
Right Angles
Measure: 90 degrees

14. Intersecting lines:
lines that cross at a point

15. Perpendicular lines:
Lines that intersect at right angles
The red and black lines below intersect at a right angle

16. Polygons

17. Polygons
A closed figure made of line segments

18. Regular Polygons
A polygon with all sides the same length
and all angles the same measure.

19. Triangles

20. Triangles:
3 sided polygons
Can be grouped by their angles
Acute triangle
Right triangles Obtuse triangles

21. Triangles:
Can be grouped by their sides
Scalene:
no sides are equal
Isosceles:
two sides are equal
Equilateral:
all sides are equal

22. Quadrilaterals

23. Quadrilaterals:
Four sided polygons
Square
Parallelograms
Rectangle
Rhombus Trapezoid

24. Other
Polygons

25. Pentagons:
Five sided polygons

26. Hexagons:
Six sided polygons

27. Heptagons:
Seven sided polygons

28. Octagon:
Eight sided polygons

29. Nonagon:
Nine sided polygons

30. Decagon:
Ten sided polygons

31. Characteristics
of Polygons

32. Comparing polygons:
Congruent figures: Shapes are
the same size, have the same
angles, and are the same
shape.

33. Comparing polygons:
Congruent figures: Shapes are the same
size, have the same angles, and are the
same shape.

34. Comparing polygons:
Similar figures: Shapes that are
the same shape but not
necessarily the same size.

35. Comparing polygons:
Similar figures: Shapes that are the same
shape but not necessarily the same size.

36. Symmetry

37. Symmetric Figures:
A shape that can be folded in half
(along the line of symmetry)
So that the two halves line up exactly.
Fold along the dotted line

38. Symmetric Figures:
A shape that can be folded in half
(along the line of symmetry)
So that the two halves line up exactly.
Other examples of symmetric figures

39. Circles

40. Circles:
• Circumference: the distance around a
circle(perimeter)
• Diameter: a line that goes through the
center of a circle
• Chord: a straight line joining two points on
the circumference of a circle
• Radius: the distance from the center to any
point on the circumference of a circle.

41. Circles:
• Circumference: the distance around a
circle(perimeter)

42. Circles:
• Diameter: a line that goes through the
center of a circle

43. Circles:
Chord: a straight line joining two points on
the circumference of a circle

44. Circles:
Radius: the distance from the center to any
point on the circumference of a circle.

45. Solids

46. Space Figures: (Solids)
A figure that has volume,
three dimensions.
Faces: flat surfaces of solids
Edges: lines where two faces meet
Vertices: the corners or points of a
solid.

47. Space Figures: (Solids)
A figure that has volume, three dimensions.
Face Edge
Vertices

48. Space Figures: (Solids)
A figure that has volume, three dimensions.

49. Perimeter
and
Area

50. Perimeter and Area:
Measuring polygons
Perimeter
Distance around a shape.
The sum of the lengths of
all sides.
Area
Square units inside a
shape

51. GPonterio PowerPoint