Geometry
Chapter 1 Review
Lessons 1.1 – 1.7
TEST Friday, October 25
Homework:
Page 90 - 92/ 1 - 32, 35 – 44
Lesson 1.1 Building Blocks of Geometry
•
Point
A location in space. No size
Line
A set of collinear points having no
endpoints. No width, only length.
Plane
A
•
B
•
C•
A set of points that creates a flat
surface that has no depth or edge.
Length & width, no height.
Collinear
A set of points that lie on a line.
A•
Coplanar
B•
A set of points, segments, lines,…
that lie on a plane.
Lesson 1.1 Building Blocks of Geometry
A
B
Line Segment A set of collinear points having
two endpoints.
A
B
X
Y
Two or more line segments that
are congruent (same size &
shape)
Midpoint of
Y
a Segment
A point that divides/bisects a
segment into two equal parts.
X
A
•
Congruent
Segments
Lesson 1.1 Building Blocks of Geometry
A
X
•
x 1, y1
A
B
•
Y Midpoint of a Segment (formula)
x 2, y2
Ray
•
Lesson 1.1 - Building Blocks of Geometry
X
X
A
•
•
B
A
•
B•
•
Angle The union of two noncollinear rays
having a common endpoint.
< AXB
Congruent
Angles
Two or more angles with the
same measure
AXB  RST means that the
•
measure of both angles are equal.
Lesson 1.1 - Building Blocks of Geometry
Angle of Reflection
The reflection of an angle will have the
same measure from the reflected surface
as the initial angle.
50o
Incoming angle
=
50o
Outgoing angle
Lesson 1.1 - Building Blocks of Geometry
Right Angle
An angle whose measure is equal 90 o.
Acute Angle An angle whose measure is < 90 o.
Obtuse Angle An angle whose measure is > 90 o.
Lesson 1.1 - Building Blocks of Geometry
Complimentary
Angles
1
1 +  2 = 90°.
2
6
7
Adjacent
Complimentary
Angles
Supplementary
Angles
4
5
Two angles whose sum of
measure equals 90°.
Two angles whose sum of
measure equals 90°.
6 +  7 = 90°.
Two angles whose sum of
measure equals 180°.
 4 +  5 = 180°.
Lesson 1.1 - Building Blocks of Geometry
1
2
8
9
Vertical
Angles
Linear Pair
of Angles
Opposite and congruent angles
formed by the intersection of two
lines.
1=2
Two adjacent supplementary
angles .
 8 +  9 = 180.
Lesson 1.1 - Building Blocks of Geometry
Polygon
A closed plane figure formed by the connecting line
segments endpoint to endpoint with each segment
intersecting exactly two other segments.
Triangle
A polygon having the fewest possible number of
sides.
n-gon
A polygon with n number of sides where n is equal to
any positive integer.
Triangle
Octagon
n=3
n=8
Lesson 1.1 - Building Blocks of Geometry
Naming Polygons
n= 5
Pentagon
n= 6
Hexagon
n= 8
Octagon
Lesson 1.1 - Building Blocks of Geometry
A
Polygon Features
B
Consecutive angles
FAB & ABC
Consecutive sides
AF & FE
Consecutive vertices
F & E
C
F
E
D
Lesson 1.1 - Building Blocks of Geometry
Diagonal of a Polygon
A
A line segment that connects two
nonconsecutive vertices of a polygon.
B
F
C
E
D
AC. AD, & AE are
each diagonals of
this polygon.
Lesson 1.1 - Building Blocks of Geometry
Groups of Polygons
Equilateral polygon
A polygon with all sides equal in length.
Equiangular polygon A polygon with all angles equal in measure.
Regular polygon
A polygon with all angles equal in measure
and all sides equal in length.
Lesson 1.1 - Building Blocks of Geometry
Groups of Polygons
Equilateral polygon
Equiangular polygon
Regular polygon
The rhombus has all
sides congruent.
The rectangle has all
angles congruent.
The square has all
angles and sides
congruent.
Lesson 1.1 - Building Blocks of Geometry
Right Triangle
Acute Triangle
A triangle with one right angle.
A triangle with three acute angles.
Lesson 1.1 - Building Blocks of Geometry
Obtuse Triangle
Scalene
Triangle
A triangle with one obtuse angle.
A triangle with no congruent sides.
Lesson 1.1 - Building Blocks of Geometry
Equilateral
Triangle
Isosceles
Triangle
A triangle with all sides congruent.
A triangle with two congruent sides.
Lesson 1.1 - Building Blocks of Geometry
Trapezoid
A quadrilateral with two sides parallel.
B
A
AB
C
D
Parallelogram
A quadrilateral with both pairs of opposites
sides parallel and congruent.
A
C
DC
B
D
AB
DC
AC
BD
Lesson 1.1 - Building Blocks of Geometry
Kite
A quadrilateral with two pair of adjacent sides
congruent.
A
D
B
C
Rhombus
A
D
A quadrilateral with opposite sides parallel
and all sides congruent.
B
C
AB
DC AB  BC  CD  DA
AD BC
Lesson 1.1 - Building Blocks of Geometry
Rectangle A parallelogram with all angle congruent (right angles).
A
B
D
AB
DC AB  DC
AD
BC AD  BC
C
A parallelogram all angles congruent and all sides
congruent.
Square
A
D
B
C
AB
DC AB  BC  CD  DA
AC
BD
Lesson 1.1 - Building Blocks of Geometry
• Circle – The set of points equidistant to
a given point.
A
F
E
B
X
D
G
C
• Radius – A segment with one endpoint
on the circle and one endpoint on the
center. XA
• Diameter – A chord that passes thru the
center of the circle. EB
• Chord – A segment whose endpoints lie
on the circle. FD
• Tangent – A line that intersects a circle
at only one point. Line GC
• Arc – The distance between two points
on a circle. AB
Lesson 1.1 - Building Blocks of Geometry
. .
A
F
E
J
B
X
D
C
Conjectures
 Through any two points there is exactly one line.
·
A
·B
 Through any three points there is at least one plane and
through any three non-collinear points there is exactly
one plane.
.A
B
.C
.
Conjectures
 If two lines intersect, then they intersect in exactly one
point.
Line l intersects line m at A.
A
l
m
A
X
B
Y
Dimensions
A line contains at least two points
A plane contains at least 3 points not in a line
Space contains at least four points not all in one plane
1 dimension
2 dimensions
3 dimensions