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Published byJeremiah Lock Modified over 3 years ago

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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 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

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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

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m n m n

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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

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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

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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

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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

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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

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

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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?

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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.

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Draw the segment that would represent the distance from the point to the line. 1. 2. 3. 4.

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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

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Assignment

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Section 3-2: Proving Lines Parallel Goal 2.02 Apply properties, definitions, and theorems of angles and lines to solve problems and write proofs.

Section 3-2: Proving Lines Parallel Goal 2.02 Apply properties, definitions, and theorems of angles and lines to solve problems and write proofs.

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