Chapter 3.1 Common Core G.CO.1 & G.CO.9 Know precise definitions of…parallel line. Prove theorems...
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Transcript of Chapter 3.1 Common Core G.CO.1 & G.CO.9 Know precise definitions of…parallel line. Prove theorems...
![Page 1: Chapter 3.1 Common Core G.CO.1 & G.CO.9 Know precise definitions of…parallel line. Prove theorems about lines and angles. Objectives – To identify relationships.](https://reader035.fdocuments.us/reader035/viewer/2022062421/56649d0a5503460f949dce11/html5/thumbnails/1.jpg)
Chapter 3.1
Common Core G.CO.1 & G.CO.9 Know precise definitions of…parallel line. Prove theorems about lines and angles.
Objectives – To identify relationships between figures in space. To identify angles formed by two lines and a transversal.
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Ch 3.1 NotesParallel Lines – 2 lines that do not intersect and are coplanar
Parallel Planes – 2 planes that do not intersect
Skew Lines – 2 lines that do not intersect and are not coplanar
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Identifying Angles Formed by Transversals
Transversal – is a line that intersects 2 or more coplanar lines at different points. Transversal
Corresponding Angles 1 2
3 4
Alternate Interior Angles 5 6
7 8
Alternate Exterior Angles
Consecutive Interior Angles(Same-Side Int. Angles)
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Chapter 3.2
Common Core G.CO.9 Prove theorems about lines and angles. Theorems include…when a transversal crosses parallel lines, alternate interior angles are congruent.
Objectives – To prove theorems about parallel lines. To use properties of parallel lines to find angles measures.
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Ch 3.2 NotesCorresponding ∠ ThmAlt. Int. ∠ ThmAlt. Ext. ∠ ThmSame-Side Int. ∠ Post.(Consecutive Int. Post.)
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Chapter 3.3
Common Core G.CO.9 Prove theorems about lines and angles. Theorems include…when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent.
Objective – To determine whether two lines are parallel.
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Ch 3.3 NotesFour ways to prove two lines are parallel.
1) Show Corr. ∠’s are ≌2) Show Alt. Int. ∠’s are ≌3) Show Alt. Ext. ∠’s are ≌4) Show Same Side are Supp. (Cons. Int. ∠’s are supp.)
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Flow Proof – is another way of proving something by using arrows and logically connections between statements
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Chapter 3.4
Common Core Common Core G.MG.3 Apply geometric methods to solve design problems.
Objective – To relate parallel and perpendicular lines.
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Ch 3.4 NotesThm – If 2 lines are parallel to the same line
then they are parallel to each other.* If p II q and q II r, then p II r. p q r
Thm – In a plane, if 2 lines are perpendicular to the same line, then they are parallel to each other.
* If m ⊥ p and n ⊥ p, then m II n.
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Perpendicular Transversal Thm – If a transversal is perpendicular to one of 2 parallel lines, then it is perpendicular to the other.
If then
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Chapter 3.5
Common Core Common Core G.CO.10 Prove theorems about triangles…measures of interior angles of a triangle sum to 180 degrees.
Objectives – To use parallel lines to prove a theorem about triangles. To find measures of angles of triangles.
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Ch 3.5 NotesTriangle Angle-Sum Theorem – the sum of the measures of the angles of a triangle is 180.
Triangle Exterior Angle Theorem – the measure of each exterior angle of a triangle equals the sum of the measures of its two remote interior angles
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Parallel 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.
If then
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Chapter 3.6
Common Core G.CO.12 & G.CO.13 Make formal geometric constructions with a variety of tools and methods…constructing perpendicular lines…and constructing a line parallel to a given line through a point not on the line.
Objective – To construct parallel and perpendicular lines.
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Ch 3.6 Notes
Constructing Parallel Lines
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Construct a Special Quadrilateral with one pair of parallel sides.
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Construct a Perpendicular at a Point on the Line
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Perpendicular Postulate – If there is a line and a point not on the line then there is exactly one line through the point and perpendicular to the given line
If then
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Construct a Perpendicular form a Point to Line
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Chapter 3.7
Common Core G.GPE.5 Prove the slope criteria for parallel and perpendicular lines.
Objective – To graph and write linear equations.
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Ch 3.7 Notes
Slope = Rise m = y – y1
Run x – x1
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Slope-intercept Form – y = mx + b where m is the slope and b is the y-intercept
Point-Slope Form – y – y1 = m(x – x1) where m is the slope and (x1,y1) is the point
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Chapter 3.8
Common Core G.GPE.5 Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems.
Objective – To relate slope to parallel and perpendicular lines.
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Ch 3.8 Notes 2 Lines are Parallel to each other if they have
the same slope.Ex. m = -4 and m1 = -4
2 Lines are Perpendicular to each other if their slopes are negative reciprocals of each other.
Ex. m = 2/3 and m1 = -3/2 then they would be perpendicular lines