Geometry Definitions and Postulates Exploration
Chapter 1.1
Common Core
G.CO.1
Know precise definitions
of angle, circle, perpendicular line, parallel line,
and line segment, based on the undefined
notions of point, line, distance along a line, and
distance around a circular arc.
Objective
– To make nets and drawings of three-
dimensional figures.
Ch 1.1 Notes
Net
– is a two-dimensional diagram that you can
fold to form a three-dimensional figure. A net
shows all of the surfaces of a figure in one view.
Isometric Drawing
– shows a corner view of a
three-dimensional figure. It allows you to see the
top, front, and side of the figure.
Orthographic Drawing
– is another way to
represent a three-dimensional figure. This
drawing shows three separate views: a top view,
a front view, and a right-side view.
Chapter 1.2
Common Core
G.CO.1
Know precise definitions of
angle, circle, perpendicular line, parallel line, and
line segment, based on the undefined notions of
point, line, distance along a line, and distance
around a circular arc.
Objective
– To understand basic terms and
postulates of geometry.
Ch 1.2 Notes
Undefined Terms – we just describe them
Point
– indicates a location & has no size,
represented by a small dot, (position in space)
Line
– is represented by a straight path that
extends in tow opposite directions without end
and has no thickness. A line contains infinitely
many points.
Plane
– is represented by a flat surface that
extends without end and has no thickness, A
plane contains infinitely many lines.
Point
Plane
Ray
Opposite Rays
Line
Line Segment
Definitions
Collinear Points
– are points all on the same line
Coplanar Points
– are points all of the same plane
Intersect
– if two or more figures have one or more
points in common
Intersection
– is the set of points the figures have
in common
Postulates or Axioms
– are rules that are accepted
without proof
Postulate 1.1
– Through any two points there is
exactly one line.
Postulate 1.2
– If two distinct lines intersect,
then they intersect in exactly one point
Postulate 1.3
– If two distinct planes intersect,
then they intersect in exactly one line.
Postulate 1.4
– Through any three points there is
exactly one plane.
Chapter 1.3
Common Core
G.CO.1 & G.GPE.6
Know precise
definitions of angle, circle, perpendicular line,
parallel line, and line segment, based on the
undefined notions of point, line, distance along a
line, and distance around a circular arc.
Objective
– To find and compare lengths of
segments.
Ch 1.3 Notes
Postulate 1.5
– Every point on a line is paired
with a real number called a coordinate.
Postulate 1.6
– Segment Addition Postulate
Lengths are equal
Segments are congruent
AB = AD
AB = AD
“is equal to”
“is congruent to”
Distance
– between two points is the absolute
value of the difference of their coordinates.
Midpoint
– of a segment is a point that divides
the segment into two congruent segments.
Segment Bisector
– is a segment or line that
cuts a segment into two equal parts.
Chapter 1.4
Common Core
G.CO.1
Know precise definitions of
angle, circle, perpendicular line, parallel line, and
line segment, based on the undefined notions of
point, line, distance along a line, and distance
around a circular arc.
Objective
– To find and compare the measures of
angles.
Ch 1.4 Notes
Angle
– consists of 2 different rays that have the
same initial point
Measures are equal
Angles are congruent
Postulate 1.8
– Angle Addition Postulate
Classifying angles by their measure
Acute angle
–
Right angle
–
Obtuse angle
–
Straight angle
–
Chapter 1.5
Common Core
G.CO.1
Know precise definitions of
angle, circle, perpendicular line, parallel line, and
line segment, based on the undefined notions of
point, line, distance along a line, and distance
around a circular arc.
Objective
– To identify special angle pairs and use
their relationships to find angle measures.
Ch 1.5 Notes
Adjacent Angles
– are 2 angles that share a
common vertex and side, but do not have any
common interior points in common
Vertical Angles
– are two angles whose sides are
opposite rays
Complementary Angles
– are two angles whose
measure have a sum of 90.
Supplementary Angles
– are two angles whose
measure have a sum of 180.
Linear Pair
– is a pair of adjacent angles whose
noncommon sides are opposite rays.
Angle Bisector
– is a ray that divides an angle into
two congruent angles.
Postulate 1.9
– If two angles form a linear pair, then
they are supplementary.
Chapter 1.6
Common Core
G.CO.12 & G.CO.1
Make formal
geometric constructions with a variety of tools and
methods
Objective
– To make basic constructions using a
straightedge and a compass.
Ch 1.6 Notes
Perpendicular Lines
– are two lines that intersect
to form right angles.
Perpendicular Bisector
– cuts a line segment into
two equal parts by a perpendicular segment,
line, or ray.
Construct the Perpendicular Bisector
Construct the Angle Bisector
Chapter 1.7
Common Core
G.GPE.4, G.GPE.7 & G.GPE.6
Use
coordinates to prove simple geometric theorems
algebraically.
Objectives
– To find the midpoint of a segment. To
find the distance between two point in the
coordinate plane.
Ch 1.7 Notes
Midpoint Formula
–
Distance Formula
-
Chapter 1.8
Common Core
N.Q.1
Use units as a way to
understand problems and to guide the solution of
multistep problems; choose and interpret units
consistently in formulas.
Objectives
– To find the perimeter or
circumference of basic shapes. To find the area of
basic shapes.
Ch 1.8 Notes
Square
-
P =
A =
Rectangle
– P =
A =
Triangle
-
P =
A =
Circle
-
C =
A =
Explore precise definitions of key geometric terms like angle, circle, perpendicular line, parallel line, and line segment, as well as essential postulates. Understand the concepts of points, lines, distances, and three-dimensional figures through nets, drawings, and visual representations.
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Presentation Transcript
Chapter 1.1 Common Core G.CO.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc. Objective To make nets and drawings of three- dimensional figures.
Ch 1.1 Notes Net is a two-dimensional diagram that you can fold to form a three-dimensional figure. A net shows all of the surfaces of a figure in one view. Isometric Drawing shows a corner view of a three-dimensional figure. It allows you to see the top, front, and side of the figure. Orthographic Drawing is another way to represent a three-dimensional figure. This drawing shows three separate views: a top view, a front view, and a right-side view.
Chapter 1.2 Common Core G.CO.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc. Objective To understand basic terms and postulates of geometry.
Ch 1.2 Notes Undefined Terms we just describe them Point indicates a location & has no size, represented by a small dot, (position in space) Line is represented by a straight path that extends in tow opposite directions without end and has no thickness. A line contains infinitely many points. Plane is represented by a flat surface that extends without end and has no thickness, A plane contains infinitely many lines.
Point Plane Ray Opposite Rays Line Line Segment
Definitions Collinear Points are points all on the same line Coplanar Points are points all of the same plane Intersect if two or more figures have one or more points in common Intersection is the set of points the figures have in common Postulates or Axioms are rules that are accepted without proof
Postulate 1.1 Through any two points there is exactly one line. Postulate 1.2 If two distinct lines intersect, then they intersect in exactly one point Postulate 1.3 If two distinct planes intersect, then they intersect in exactly one line. Postulate 1.4 Through any three points there is exactly one plane.
Chapter 1.3 Common Core G.CO.1 & G.GPE.6 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc. Objective To find and compare lengths of segments.
Ch 1.3 Notes Postulate 1.5 Every point on a line is paired with a real number called a coordinate. Postulate 1.6 Segment Addition Postulate Lengths are equal AB = AD Segments are congruent AB = AD is equal to is congruent to
Distance between two points is the absolute value of the difference of their coordinates. Midpoint of a segment is a point that divides the segment into two congruent segments. Segment Bisector is a segment or line that cuts a segment into two equal parts.
Chapter 1.4 Common Core G.CO.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc. Objective To find and compare the measures of angles.
Ch 1.4 Notes Angle consists of 2 different rays that have the same initial point Measures are equal Angles are congruent
Postulate 1.8 Angle Addition Postulate Classifying angles by their measure Acute angle Right angle Obtuse angle Straight angle
Chapter 1.5 Common Core G.CO.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc. Objective To identify special angle pairs and use their relationships to find angle measures.
Ch 1.5 Notes Adjacent Angles are 2 angles that share a common vertex and side, but do not have any common interior points in common
Vertical Angles are two angles whose sides are opposite rays Complementary Angles are two angles whose measure have a sum of 90. Supplementary Angles are two angles whose measure have a sum of 180.
Linear Pair is a pair of adjacent angles whose noncommon sides are opposite rays. Angle Bisector is a ray that divides an angle into two congruent angles. Postulate 1.9 If two angles form a linear pair, then they are supplementary.
Chapter 1.6 Common Core G.CO.12 & G.CO.1 Make formal geometric constructions with a variety of tools and methods Objective To make basic constructions using a straightedge and a compass.
Ch 1.6 Notes Perpendicular Lines are two lines that intersect to form right angles. Perpendicular Bisector cuts a line segment into two equal parts by a perpendicular segment, line, or ray.
Chapter 1.7 Common Core G.GPE.4, G.GPE.7 & G.GPE.6 Use coordinates to prove simple geometric theorems algebraically. Objectives To find the midpoint of a segment. To find the distance between two point in the coordinate plane.
Ch 1.7 Notes Midpoint Formula Distance Formula -
Chapter 1.8 Common Core N.Q.1 Use units as a way to understand problems and to guide the solution of multistep problems; choose and interpret units consistently in formulas. Objectives To find the perimeter or circumference of basic shapes. To find the area of basic shapes.
Ch 1.8 Notes Square - P = A = Rectangle P = A = Triangle - P = A = Circle - C = A =
