# Geometry Fall 2020 Lesson 031 Properties Of Parallel Lines

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1Lesson Plan #31Class: GeometryDate: Thursday December 17th, 2020Topic: Properties of parallel lines?Aim: What are some properties of parallel lines?Objectives:1) Students will be able to use properties of parallel lines.HW #31: Pages 5 and 6 of this lesson planNote:Postulate for inequalitiesIf π, π, π and π are real numbers, such thatπ π and π π, then π π π π orif unequal quantities are added to unequal quantities of the same order, the sums are unequal in the sameorder.For example, if 7 5and 3 2, then 7 3 5 2PostulateIf a, b, c and d are real numbers, such that π π and π π, then π π π π orif equal quantities are subtracted from unequal quantities, the differences are unequal in the same order.For example,7 5and 2 2, then 7 2 5 2Do Now:Assignment:Using a straight edge, draw two lines, then draw a third line thatintersecting the first two lines.PROCEDURE:Write the Aim and Do NowGet students working!Take attendanceGive Back HWCollect HWGo over the Do NowWhat do we call the line that intersects two or more coplanar lines in different points?Definition: A transversal is a line that intersects two or more coplanar lines in different points.3How many angles are formed?Which angles are in the interior of the two lines?5 6Which angles are exterior to the two lines?Which are pairs of alternate interior angles?Define alternate interior angles.Which are pairs of alternate exterior angles?Define alternate exterior angles.Which are pairs of interior angles on the same side of the transversal?4

2Definition: Corresponding angles are a pair of angles on the same side ofthe transversal, not sharing a common vertex, and one is interior and one isexterior.Name pairs of corresponding angles:5Letβs examine parallel lines.Online Interactive Activity:Letβs go ion: Parallel lines are coplanar lines that donot intersect or coplanar lines are parallel if and onlyif they have no points in common or if the linescoincide and, therefore, have all points in common.Skew LinesDefinition of Skew Lines Two nonparallel lines in space that do not intersect are called skew lines.Skew lines are non-coplanar lines. Therefore, they are neither parallel nor intersectingExamples of Skew Lines are skew lines in the figure shown.Solved Example on Skew LinesWhich of the following are skew lines?Choices:A.andB.andC.andD.and3Source: http://www.icoachmath.com/math dictionary/Skew Lines.htmlβ‘ πΆπ·β‘How would you read the notation at right? π΄π΅If two coplanar lines are not parallel, then what can we say aboutthose two lines?Theorem: If coplanar lines are not parallel lines, then theyare intersecting lines.Is Parallelism an equivalence relation? In other words, does it satisfythe reflexive property, symmetric property and transitive property?mnr64

3Postulates:A line is parallel to itselfA parallelism of lines may be expressed in either orderTwo lines each parallel to same line are parallel to each other.Hands on Activity:PDraw a line parallel to the given line through the point not on the lineHow many lines can you draw through π andparallel to π?mTheorem: Through a given point not on a given line, there exists one and only one line parallel to thegiven line.Hands on Activity:Animation of construction at βs see how we can construct a line parallel to a given line through a given external point.PmSteps:After doing thisStart with a line PQ and a point R off the line.1. Draw a transverse line through R and across the line PQ at an angle,forming the point J where it intersects the line PQ. The exact angle is notimportant.2. With the compass width set to about half the distance between R andJ, place the point on J, and draw an arc across both lines.Your work should look like this

4After doing thisYour work should look like this3. Without adjusting the compass width, move the compass to R anddraw a similar arc to the one in step 2.4. Set compass width to the distance where the lower arc crosses thetwo lines.5. Move the compass to where the upper arc crosses the transverse lineand draw an arc across the upper arc, forming point S.6. Draw a straight line through points R and S.Done. The line RS is parallel to the line PQGiven the parallel lines at right, is it possible to draw a line intersectingone line but not the other?Theorem: If a line intersects one of two parallel lines, it intersects the other.Assignment: A parallelogram is a quadrilateral with both pair of opposite sides parallel. Construct a parallelogram inthe space below

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Sep 15, 2020Β Β· Two nonparallel lines in space that do not intersect are called skew lines. Skew lines are non-coplanar lines. Therefore, they are neither parallel nor intersecting Examples of Skew Lines are skew lines in the figure shown. Solved Example on Skew Lines Which of the following are skew

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