2. GeometryGeometry
• the branch of mathematics
that is concerned with the
properties of
configurations of
geometric objects –
points, (straight) lines,
and circles.

3. GeometryGeometry
• The word ‘geometry’
comes from the Greek
words geo, meaning earth,
and metria, meaning
measure.

4. A Greek
mathematician
who lived around
the year 300 BC is
often referred to
as the Father of
Geometry for his
amazing geometry
works that
included his
influential book,
‘Elements’.

5. Types of GeometryTypes of Geometry
• Plane geometryPlane geometry deals with
objects that are flat, such as
triangles and lines, that can be
drawn on a flat piece of paper in
two dimensions.
• Solid geometrySolid geometry deals with
objects in that space, having
width, depth and height, such as
cubes and spheres.

6. Tools of GeometryTools of Geometry
• The compass and
straight edge were
powerful tools in the
advancement of
geometry, allowing
the construction of
various lengths,
angles and
geometric shapes.

7. Geometry in Real LifeGeometry in Real Life

8. Geometry in ActionGeometry in Action
• Design and
manufacturing
– Architecture
– Assembly planning
– CAD/CAM
– Robotics
– Modeling
– Textile layout
– VLSI design
• Graphics and
visualization
– Computer
graphics
– Graph drawing
– Virtual reality
– Video game
programming

9. Geometry in ActionGeometry in Action
• Medicine and
biology
– Medical imaging
– Biochemical
modeling
• Information
systems
– Cartography and
geographic
information
systems
– Data mining and
multidimensional
analysis
• Physical
sciences
– Astronomy
– Molecular

10. CAD/CA
M
Architectu
re
VLSI
design
Textile
layout Biomedical
imaging
Cartograph
y
Molecular
modeling

11. Lines, Points andLines, Points and
PlanesPlanes

12. PointsPoints
• A point has no dimension.
• It is usually represented by a
small dot.
A

13. LinesLines
• A line extends in one dimension.
• It is usually represented by a
straight line with two arrowheads
to indicate that the line extends
without end in two directions.
Line l or AB
B
l
A

14. LinesLines
• Collinear points are points that
lie on the same line.
• Points A, B, and C are collinear.
C Line
l
A B

15. LinesLines
• The line segment or segment AB
(symbolized by AB) consists of
the endpoints A and B, and all
points on AB that are between A
and B.
C
Line
l
A
B
A B
Segment
AB

16. LinesLines
• The ray AB (symbolized by BC)
consists of the initial point B and
all points on Line l that lie on the
same side of B as point C.
C
Line
l
A B
CB
Ray
BC

17. PlanesPlanes
• A plane extends
in two
dimensions.
• The plane
extends without
end even though
the drawing of a
plane appears to
have edges.
A
B
C
M

18. PlanesPlanes
• A plane extends
in two
dimensions.
• The plane
extends without
end even though
the drawing of a
plane appears to
have edges.
A
B
C
M
• Coplanar points are
points that lie on the same
plane.

19. PlanesPlanes
• D, E, F, and G lie
on the same
plane, so they
are coplanar.
• D, E, F, and H are
also coplanar;
although, the
plane containing
them is not
drawn.
G
D
E F
H

20. PlanesPlanes
A line intersects a
plane
in one point.

21. PlanesPlanes
Two planes
intersect
plane in a line.

22. Parallel Lines,Parallel Lines,
Transversals andTransversals and
AnglesAngles

23. Parallel LinesParallel Lines
Two lines are parallel lines if they
are coplanar and do not
intersect.

24. Parallel PostulateParallel Postulate
• If there is a line and a point not
on the line, then there is exactly
one line through the point
parallel to the given line.
ll
PP

25. TransversalTransversal
A line that intersects two or more
coplanar lines at different points.
P1
P2

26. Transversal and AnglesTransversal and Angles
• Angle 1 and 5 are
corresponding
angles
• Angles 1 and 8 are
alternate exterior
angles
• Angles 3 and 5 are
alternate interior
angles.
1 2
5 6
7 8
3 4
• Angles 3 and 5
are consecutive
interior angles.

27. Corresponding AnglesCorresponding Angles
PostulatePostulate
If two parallel lines are cut by a
transversal, then the pairs of
corresponding angles are
congruent.
2
1 l
m
If l // m, then ∠ 1 ≅ ∠ 2.

28. Alternate Interior AnglesAlternate Interior Angles
TheoremTheorem
If two parallel lines are
cut by a transversal, then
the pairs of alternate
interior ∠s are ≅.
2
1
l
m
If l // m, then ∠1 ≅ ∠2.