Geometry

1
Geometry

• Chapter 1 Review
• Lessons 1.1 1.7
• TEST Friday, October 25
• Homework
• Page 90 - 92/ 1 - 32, 35 44

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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.
A set of points that creates a flat surface that
has no depth or edge. Length width, no height.
Plane
Collinear
A set of points that lie on a line.
Coplanar
A set of points, segments, lines, that lie on a
plane.
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Lesson 1.1 Building Blocks of Geometry
A set of collinear points having two endpoints.
Line Segment
A
B
Congruent Segments
Two or more line segments that are congruent
(same size shape)
X
Y
Midpoint of a Segment
A point that divides/bisects a segment into two
equal parts.

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Lesson 1.1 Building Blocks of Geometry

Midpoint of a Segment (formula)
x 1, y1
x 2, y2
 
B
Ray

 

H
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Lesson 1.1 - Building Blocks of Geometry
Angle
The union of two noncollinear rays having a
common endpoint. lt AXB



Congruent Angles
Two or more angles with the same measure


?AXB ? ?RST means that the measure of both angles
are equal.

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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 Outgoing angle
50o
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Lesson 1.1 - Building Blocks of Geometry
An angle whose measure is equal 90 o.
Right Angle
Acute Angle
An angle whose measure is lt 90 o.
Obtuse Angle
An angle whose measure is gt 90 o.
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Lesson 1.1 - Building Blocks of Geometry
Complimentary Angles
Two angles whose sum of measure equals 90. ?1
? 2 90.
1
2
Two angles whose sum of measure equals 90. ?6
? 7 90.
Adjacent Complimentary Angles
Two angles whose sum of measure equals 180. ?
4 ? 5 180.
Supplementary Angles
4
5
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Lesson 1.1 - Building Blocks of Geometry
Vertical Angles
Opposite and congruent angles formed by the
intersection of two lines. ? 1 ? 2
1
2
Linear Pair of Angles
Two adjacent supplementary angles . ? 8 ? 9
180.
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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.
A polygon having the fewest possible number of
sides.
Triangle
n-gon
A polygon with n number of sides where n is equal
to any positive integer.
Octagon
Triangle
n 3
n 8
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Lesson 1.1 - Building Blocks of Geometry
Naming Polygons
n 5
Pentagon
Hexagon
n 6
Octagon
n 8
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Lesson 1.1 - Building Blocks of Geometry
Polygon Features
Consecutive angles
?FAB ?ABC
Consecutive sides
Consecutive vertices
?F ?E
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Lesson 1.1 - Building Blocks of Geometry
Diagonal of a Polygon
A line segment that connects two nonconsecutive
vertices of a polygon.
AC. AD, AE are each diagonals of this polygon.
 
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Lesson 1.1 - Building Blocks of Geometry
Groups of Polygons
A polygon with all sides equal in length.
Equilateral polygon
A polygon with all angles equal in measure.
Equiangular polygon
A polygon with all angles equal in measure and
all sides equal in length.
Regular polygon
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Lesson 1.1 - Building Blocks of Geometry
Groups of Polygons
Equilateral polygon
The rhombus has all sides congruent.
The rectangle has all angles congruent.
Equiangular polygon
The square has all angles and sides congruent.
Regular polygon
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Lesson 1.1 - Building Blocks of Geometry
Right Triangle
A triangle with one right angle.
Acute Triangle
A triangle with three acute angles.
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Lesson 1.1 - Building Blocks of Geometry
Obtuse Triangle
A triangle with one obtuse angle.
Scalene Triangle
A triangle with no congruent sides.
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Lesson 1.1 - Building Blocks of Geometry
Equilateral Triangle
A triangle with all sides congruent.
Isosceles Triangle
A triangle with two congruent sides.
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Lesson 1.1 - Building Blocks of Geometry
Trapezoid
A quadrilateral with two sides parallel.
B
A
C
D
A quadrilateral with both pairs of opposites
sides parallel and congruent.
Parallelogram
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Lesson 1.1 - Building Blocks of Geometry
Kite
A quadrilateral with two pair of adjacent sides
congruent.
A quadrilateral with opposite sides parallel and
all sides congruent.
Rhombus
A
B
D
C
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Lesson 1.1 - Building Blocks of Geometry
Rectangle
A parallelogram with all angle congruent (right
angles).
A
B
D
C
A parallelogram all angles congruent and all
sides congruent.
Square
A
B
D
C
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Lesson 1.1 - Building Blocks of Geometry

• Circle The set of points equidistant to a given
  point.
• 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

A
F
B
E
X
D
C
G
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Lesson 1.1 - Building Blocks of Geometry
.
.

•  

A
J
F
B
E
X
D
C
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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

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Conjectures

• If two lines intersect, then they intersect in
  exactly one point.

Line l intersects line m at A.
 
A
Y
X
B
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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