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Sections 3.2 and 3.3 Parallel Lines & Transversals Geometry Mr. Robinson Fall 2011
Essential Question: What results can be determined when parallel lines are cut by a transversal?
Postulate 15 Corresponding s Post. If 2 lines are cut by a transversal, then the pairs of corresponding s are . i.e. If l m, then 1 2. l m 1 2
Section 3.2 Theorems Theorem 3.1 – If two lines intersect to form a linear pair of congruent angles, then the lines are perpendicular.
Section 3.2 Theorems Theorem 3.2 – If two sides of two adjacent acute angles are perpendicular, then the angles are complementary.
Section 3.2 Theorems Theorem 3.3 – If two lines are perpendicular, then they intersect to form four right angles.
Theorem 3.4 Alternate Interior s Theorem If 2 lines are cut by a transversal, then the pairs of alternate interior s are . i.e. If l m, then 1 2. lmlm 1 2
Theorem 3.5 Consecutive Interior s Theorem If 2 lines are cut by a transversal, then the pairs of consecutive int. s are supplementary. i.e. If l m, then 1 & 2 are supp. lmlm 1 2
Theorem 3.6 Alternate Exterior s Theorem If 2 lines are cut by a transversal, then the pairs of alternate exterior s are . i.e. If l m, then 1 2. l m 1 2
If a transversal is to one of 2 lines, then it is to the other. i.e. If l m, & t l, then t m. ** 1 & 2 added for proof purposes. 1 2 Theorem 3.7 Transversal Theorem lmlm t
Ex: Find: m 1= m 2= m 3= m 4= m 5= m 6= x= 125 o x+15 o
Ex: Find: m 1=55 ° m 2=125 ° m 3=55 ° m 4=125 ° m 5=55 ° m 6=125 ° x=40 ° 125 o x+15 o
Assignment Pp. 138 – 139 #3-16 pp #1-26
PARALLEL LINES AND TRANSVERSALS SECTIONS
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Angles and Parallel Lines Corresponding Angle Postulate If two parallel lines are crossed by a transversal, then each pair of corresponding.
Parallel Lines are two or more lines that do not intersect.
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Warm Up Week 1 1) If ∠ 1 and ∠ 2 are vertical angles, then ∠ 1 ≅ ∠ 2. State the postulate or theorem: 2) If ∠ 1 ≅ ∠ 2 and ∠ 2 ≅ ∠ 3, then ∠ 1.
IDENTIFY PAIRS OF LINES AND ANGLES SECTION
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Angle Relationships. Vocabulary Transversal: a line that intersects two or more lines at different points. Transversal: a line that intersects two or.
1 Angles and Parallel Lines. 2 Transversal Definition: A line that intersects two or more lines in a plane at different points is called a transversal.
Chapter 3.1 Notes Parallel Lines – 2 lines that do not intersect and are coplanar Parallel Planes – 2 planes that do not intersect Skew Lines – 2 lines.
1.3b- Angles with parallel lines G-CO.9 Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses.
PARALLEL LINES AND TRANSVERSALS. CORRESPONDING ANGLES POSTULATE Two lines cut by a transversal are parallel if and only if the pairs of corresponding.
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3.2: Properties of Parallel Lines 1. Today’s Objectives Understand theorems about parallel lines Use properties of parallel lines to find angle measurements.
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Lesson 4-2 Parallel Lines and Transversals. Ohio Content Standards:
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Lines that are coplanar and do not intersect. Parallel Lines.
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Warm-Up Classify the angle pair as corresponding, alternate interior, alternate exterior, consecutive interior or.
1Geometry Lesson: Aim: How do we prove lines are parallel? Do Now: 1) Name 4 pairs of corresponding angles. 2) Name 2 pairs of alternate interior angles.
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GEOMETRY UNIT 3 VOCABULARY ALL ABOUT ANGLES. ANGLE DEFINITION Angle A figure formed by two rays with a common endpoint.
3.1 Lines and Angles Objective: Students will identify the relationships between 2 lines or 2 planes, and name angles formed by parallel lines and transversals.
3.2 Proof and Perpendicular Lines. Let’s Review Theorem 2.6-Vertical Angles Theorem Vertical angles are congruent…. Given: <5 & <6 are a linear pair;
Coplanar lines that do not intersect.. Lines that do not intersect and are not coplanar.
Proving Lines Parallel Section 3-5. Postulate 3.4 If 2 lines are cut by a transversal so that corresponding angles are congruent, then the lines are parallel.
Line and Angle Relationships Sec 6.1 GOALS: To learn vocabulary To identify angles and relationships of angles formed by tow parallel lines cut by a transversal.
Chapter 12 and Chapter 3 Geometry Terms. Adjacent and Vertical Angles Two angles are adjacent angles when they share a common side and have the same vertex.
3-3 Proving Lines Parallel. Converse of the Corresponding Angles Theorem Theorem: If two lines and a transversal form corresponding angles that are congruent,
CHAPTER 4 Parallels. Parallel Lines and Planes Section 4-1.
3.5 Proving Lines Parallel. Objectives Recognize angle conditions that occur with parallel lines Prove that two lines are parallel based on given angle.
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