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Assumption High School

BELL WORK




Geometry2016 – 2017

Day 28Topic: Test 1.5 on Chapter 3-1 to 3-5



Chapter 3 Big Ideas

•Reasoning and Proof• How do you prove that two lines are Parallel?

•Measurement• What is the measure of the sum of all the angles in a

Triangle?

•Coordinate Geometry• How do you write an equation of a line in the coordinate

plane?



Common Core State StandardsGeometry (GM)

• Experiment with transformations in the plane• GM: G-CO.A.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.

• Use coordinates to prove simple geometric theorems algebraically.• GM: G-CO.C.9: Prove and apply theorems about lines and angles. Theorems

include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment’s endpoints.



Student Objectives

• I can identify relationships between figures in space.

• I can identify angles formed by two lines and a transversal.

• I can identify special relationships between angles formed by two lines and a transversal.

• I can identify real life objects that model parallel lines, skew lines, and parallel planes.

• I can solve algebraic expressions to find the measure of angles formed by parallel lines and a transversal.

• I can identify the relationship between parallel and perpendicular lines.

• I can graph and write linear equations.

• I can relate slope to parallel and perpendicular lines.



Chapter 3 Parallel and Perpendicular Lines

• Parallel Lines

• Skew Lines

• Parallel Planes

• Transversal

• Alternate Interior Angles

• Same-side Interior Angles

• Corresponding Angles

• Alternate Exterior Angles

• Postulate 3-1 Same-Side Interior Angles Postulate

• Theorem 3-1 Alternate Interior Angles Theorem

• Theorem 3-2 Corresponding Angles Theorem

• Theorem 3-3 Alternate Exterior Angles Theorem

• Theorem 3-4 Converse of the Corresponding Angles Theorem

• Theorem 3-5 Converse of the Alternate Interior Angles Theorem

• Theorem 3-6 Converse of the same-Side Interior Angles Postulate

• Theorem 3-7 Converse of the Alternate Exterior Angles Theorem



Chapter 3 continued…

• Key Concepts• Theorem 3-8

• Theorem 3-9

• Theorem 3-10 Perpendicular Transversal Theorem

• Auxiliary Line

• Exterior Angle of a Polygon

• Remote Interior Angles

• Postulate 3-2 Parallel Postulate

• Theorem 3-11 Triangle Angle-Sum Theorem

• Theorem 3-12 Triangle Exterior Angle Theorem



Lines and Angles

•Parallel Lines are coplanar lines that do not intersect. (p140)

• The symbol means ”is parallel to.”

•Skew Lines are noncoplanar; they are not parallel and do not intersect (p140)

•Parallel Planes are planes that do not intersect. (p140)



Lines and Angles continued…

•Transversal a line that intersects two or more coplanar lines at distinct points.



Angle Pairs formed by a Transversal

• p143



Postulate 3-1

•Same-Side Interior Angles Postulate•If a transversal intersects two parallel lines, then same-side interior angles are supplementary



Theorem 3-1

•Alternate Interior Angle Theorem•If a transversal intersects two parallel lines, then alternate interior angles are congruent



Theorem 3-2

•Corresponding Angles Theorem•If a transversal intersects two parallel lines, then corresponding angles are congruent



Theorem 3-3

•Alternate Exterior Angles Theorem•If a transversal intersects two parallel lines, then alternate exterior angles are congruent



Theorem 3-4

•Converse of the Corresponding Angles Theorem•If two lines and a transversal form corresponding angles that are congruent, then the lines are parallel



Theorem 3-5

•Converse of the Alternate Interior Angles Theorem•If two lines and a transversal form alternate interior angles that are congruent, then two lines are parallel



Theorem 3-6

•Converse of the Same Side Interior Angle Postulate•If two lines and a transversal form same-side interior angles that are supplementary, then the two lines are parallel



Theorem 3-7

•Converse of the Alternate Exterior Angles Theorem• If two lines and a transversal form alternate exterior angles that are congruent, then the two lines are parallel



Theorem 3-8

•Theorem• If two lines are parallel to the same line, then they are parallel to each other.



Theorem 3-9

•Theorem• In a plane, if two lines are perpendicular to the same line, then they are parallel to each other



Theorem 3-10

•Perpendicular Transversal Theorem• In a plane, if a line is perpendicular to one of two parallel lines, then it is also perpendicular to the other



Vocabulary

• Auxiliary Line - a line that you add to a diagram to help explain the relationship in proofs.

• Exterior Angle of a Polygon - an angle formed by a side and an extension of an adjacent side.

• Remote Interior Angles - in a triangle, the two nonadjacent interior angles to an exterior angle.



Postulate 3-2 Parallel Postulate

• Through a point not on a line, there is one and only one parallel to the given line.

• There is exactly one line through P parallel to L

P

L



Theorem 3-11 Triangle Angle-Sum Theorem

• The sum of the measure of the angles of a triangle is 180.



Theorem 3-12 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



Testing Procedures

• Take out at least two #2 lead pencils.

• You may only keep your Learning Log (Composition Notebook) out on your desk.

• You will maintain silence throughout the entire test.

• If you have a question, raise your hand and I will come to you.

• Once you complete the test, you will turn it in to me and immediately return to your seats.

• Upon completion, you will have instructions on the board.



Test in Progress!!!

•Remain seated

•Remain quiet

•Eyes on your own paper

•Good Luck!!!



To be continued…

• Tomorrow, we will resume working on Chapter 3-7 & 3-8

• Homework: Enjoy your evening without homework.

• Your next test (1.6) on Chapter 3-7 to 3-8 will be Thursday 02/23/2017.

• Visit our website for resources to help prepare you for your test.

http://fordmathletes.weebly.com/

http://fordmathletes.weebly.com/



Slope of a Line

•Often referred to as Rise over Run, the slope refers to the ratio of change in X values and change in Y values on a line.



Slope Formulas



Point Slope Form

•Point Slope Form is used if you have the coordinates to one known point and you have a value for the slope of a line.

• The point-slope form of an equation of a nonvertical line is



Slope Intercept Form

•The slope-intercept form of an equation of a nonvertical line is

y = mx + b



Standard Form

•The Standard Form for a linear equation in two variables, x and y, is usually given as.

Ax + By = C. where, if at all possible, A, B, and C are integers, and A is non-negative, and, A, B, and C have no common factors other than 1



3-8 Key Concepts

• Slopes of Parallel Lines• If two nonvertical lines are parallel, then their slopes are equal

• If the slopes of two distinct nonvertical lines are equal, then the lines are parallel.

• Any two vertical lines or horizontal lines are parallel.

• Slopes of Perpendicular Lines• If two nonvertical lines are perpendicular, then the product of their

slopes is -1.

• If the slopes of two lines have a product of -1, then the lines are perpendicular.

• Any horizontal line and vertical line are perpendicular.



We are a TEAM

• Remember what it mean to be part of a team…

•Together

•Everyone

•Achieves

•More

Mr. Matthew J Ford



Following rules means being HAPPY

• Being HAPPY means being:

• Honest

• Accountable

• Proactive

• Positive

• Yourself

Mr. Matthew J Ford



Any Questions???



You guy Rock!!!

•I Love all you crazy kiddos…

•You guys are real Mathletes in Training!

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