chapter 1.1 common core g.co.1 know precise definitions of angle, circle, perpendicular line,...
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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.
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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.
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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.
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Ch 1.2 NotesUndefined 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.
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Point
Plane
Ray
Opposite Rays
Line
Line Segment
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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
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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.
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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.
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Ch 1.3 NotesPostulate 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 congruentAB = AD AB = AD“is equal to” “is congruent to”
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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.
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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.
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Ch 1.4 Notes
Angle – consists of 2 different rays that have the same initial point
Measures are equal Angles are congruent
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Postulate 1.8 – Angle Addition Postulate
Classifying angles by their measureAcute angle –Right angle –Obtuse angle –Straight angle –
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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.
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Ch 1.5 NotesAdjacent Angles – are 2 angles that share a
common vertex and side, but do not have any common interior points in common
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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.
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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.
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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.
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Ch 1.6 NotesPerpendicular 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.
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Construct the Perpendicular Bisector
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Construct the Angle Bisector
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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.
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Ch 1.7 Notes
Midpoint Formula –
Distance Formula -
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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.
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Ch 1.8 NotesSquare - P =
A =
Rectangle – P = A =
Triangle - P =A =
Circle - C = A =