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1.4c: Lines and Angle Relationships -proving lines parallel GSE’s M(G&M)–10–2 Makes and defends conjectures, constructs geometric arguments, uses geometric.

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Presentation on theme: "1.4c: Lines and Angle Relationships -proving lines parallel GSE’s M(G&M)–10–2 Makes and defends conjectures, constructs geometric arguments, uses geometric."— Presentation transcript:

1 1.4c: Lines and Angle Relationships -proving lines parallel GSE’s M(G&M)–10–2 Makes and defends conjectures, constructs geometric arguments, uses geometric properties, or uses theorems to solve problems involving angles, lines, polygons, M(G&M)–10–9 Solves problems off the coordinate plane involving distance, midpoint, perpendicular and parallel lines, or slope

2 Corresponding  s If 2 lines are cut by a transversal so that corresponding  s are , then the lines are . ** If  1   2, then l  m. lmlm 1 2

3 m n m n

4 Alt. Ext.  s Converse If 2 lines are cut by a transversal so that alt. ext.  s are , then the lines are . ** If  1   2, then l  m. lmlm 1 2

5 Consecutive Int.  s Converse If 2 lines are cut by a transversal so that consecutive int.  s are supplementary, then the lines are . ** If  1 &  2 are supplementary, then l  m. 1 2 lmlm

6 Alt. Int.  s Converse If 2 lines are cut by a transversal so that alt. int.  s are , then the lines are . ** If  1   2, then l  m. 1 2 lmlm

7 Ex: Based on the info in the diagram, is p  q ? If so, give a reason. Yes, alt. ext.  s conv. No p q p q p q

8 Ex: Find the value of x that makes j  k. The angles marked are consecutive interior  s. Therefore, they are supplementary. x + 3x = 180 4x = 180 x = 45 j k x o 3x o

9 Are there any parallel lines In this bookcase? How do you know?

10

11 Suppose that maple Street and Oak Street follow a straight line path and intersect Route 6 at angles 90º and 85º, as shown in the map below. If the streets continue in a straight line, will their paths ever cross?

12 Distance between a point & line The shortest distance between a point and A line is its perpendicular segment R V m The distance from Point R to line m is VR.

13 Draw the segment that would represent the distance from the point to the line

14 Name the segment whose length represents the distance between the following points and lines. 1) A to BC 2) C to AB 3) B to AC 4) N to BC

15 Assignment


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