2
Most read
5
Most read
6
Most read
Parallel Lines & Transversals
The student is able to (I can):
• Identify parallel lines, perpendicular lines, skew lines, and
parallel planes
• Identify
– Transversals
– Corresponding angles
– Alternate Interior Angles
– Alternate Exterior Angles
– Consecutive Interior Angles
parallelparallelparallelparallel lineslineslineslines – coplanar lines that do not intersect
perpendicularperpendicularperpendicularperpendicular lineslineslineslines – two coplanar lines that intersect at right
angles (90˚)
m
n
m n
f
g f ⊥ g
⊥ means
“perpendicular”
means “parallel”
skewskewskewskew lineslineslineslines – noncoplanar lines that do not intersect
parallelparallelparallelparallel planesplanesplanesplanes – planes that do not intersect
R
S
Plane R Plane S
transversaltransversaltransversaltransversal – a line that intersects two coplanar lines at two
different points
r
s
t
correspondingcorrespondingcorrespondingcorresponding anglesanglesanglesangles – angles that lie on the same side of the
transversal t, on the same sides of lines r and s
Example: ∠1 and ∠5
CorrespondingCorrespondingCorrespondingCorresponding anglesanglesanglesangles of parallel lines are congruent.of parallel lines are congruent.of parallel lines are congruent.of parallel lines are congruent.
87 6
5
4
3
1
2
∠1 ≅ ∠5
∠2 ≅ ∠6
∠3 ≅ ∠7
∠4 ≅ ∠8
t
s
r
alternate interioralternate interioralternate interioralternate interior anglesanglesanglesangles – angles that lie on opposite sides of
the transversal t, between lines r and s
Example: ∠2 and ∠7 or ∠4 and ∠5
Alternate interior anglesAlternate interior anglesAlternate interior anglesAlternate interior angles of parallel lines are congruent.of parallel lines are congruent.of parallel lines are congruent.of parallel lines are congruent.
r
s
t
interior
8
7 6
5
4
3
1
2 ∠2 ≅ ∠7
∠4 ≅ ∠5
alternate exterioralternate exterioralternate exterioralternate exterior anglesanglesanglesangles – angles that lie on opposite sides of
the transversal t, outside lines r and s
Example: ∠1 and ∠8
Alternate exterior anglesAlternate exterior anglesAlternate exterior anglesAlternate exterior angles of parallel lines are congruent.of parallel lines are congruent.of parallel lines are congruent.of parallel lines are congruent.
r
s
t
exterior
exterior
8
7
6
5
4
3
1
2
∠1 ≅ ∠8
∠4 ≅ ∠5
consecutive interiorconsecutive interiorconsecutive interiorconsecutive interior anglesanglesanglesangles – angles that lie on the same side
of the transversal t, between the lines r and s.
Example: ∠3 and ∠5
ConsecutiveConsecutiveConsecutiveConsecutive interior anglesinterior anglesinterior anglesinterior angles of parallel lines areof parallel lines areof parallel lines areof parallel lines are supplementary.supplementary.supplementary.supplementary.
r
s
t
interior
87
65
43
1 2
m∠3 + m∠5 = 180˚
m∠4 + m∠6 = 180˚
consecutiveconsecutiveconsecutiveconsecutive exterior anglesexterior anglesexterior anglesexterior angles – angles that lie on the same side
of the transversal t, outside the lines r and s.
Example: ∠2 and ∠8
ConsecutiveConsecutiveConsecutiveConsecutive exterior anglesexterior anglesexterior anglesexterior angles of parallel lines areof parallel lines areof parallel lines areof parallel lines are supplementary.supplementary.supplementary.supplementary.
r
s
t
interior
87
65
43
1 2
m∠1 + m∠7 = 180˚
m∠2 + m∠8 = 180˚
1. Find the measures of the
numbered angles if
m∠8 = 125˚
2. List each angle pair
corresponding angles
alt. interior angles
alt. exterior angles
consecutive interior angles
1 2
3 8
4 5
6 7
Examples
1. Find the measures of the
numbered angles if
m∠8 = 125˚
m∠1 = 125˚; m∠2 = 55˚;
m∠3 = 55˚; m∠4 = 125˚;
m∠5 = 55˚; m∠6 = 55˚;
m∠7 = 125˚
2. List each angle pair
corresponding angles
∠1 & ∠4; ∠2 & ∠5;
∠3 & ∠6; ∠8 & ∠7
alt. interior angles
∠3 & ∠5; ∠8 & ∠4
alt. exterior angles
∠1 & ∠7; ∠2 & ∠6
consecutive interior angles
∠3 & ∠4; ∠8 & ∠5
1 2
3 8
4 5
6 7
Examples

More Related Content

PPTX
Triangle Sum Theorem
PPTX
Parallel Line
PPT
Angle relationships
PPTX
Parallel Line Properties
PPTX
Parallel and perpendicular lines
PPTX
Congruent Triangles
PPTX
1.7 angles and perpendicular lines
PPTX
Geometric Transformation: Reflection
Triangle Sum Theorem
Parallel Line
Angle relationships
Parallel Line Properties
Parallel and perpendicular lines
Congruent Triangles
1.7 angles and perpendicular lines
Geometric Transformation: Reflection

What's hot (20)

PPT
Parallel lines and transversals
PPTX
Real Number System
PPT
Square and square roots
PPSX
Congruent triangles theorem
PPTX
Angles: Naming, Types, and How to Measure Them
PPTX
Parallel Lines Cut by a Transversal PPT 1-9-2018.pptx
PPT
Absolute values
PPT
Linear Inequality
PDF
Radical expressions
PPTX
Pairs of Angles
PPT
Coordinate plane ppt
PPT
Congruent triangles
PPT
Similar Figures
PPTX
Direct and inverse proportion
PPT
1.2 Irrational Numbers ppt
PDF
2.5.5 Perpendicular and Angle Bisectors
PPT
Distance between two points
PPTX
Algebraic expression
PDF
Arc length, area of a sector and segments of a circle
PPT
Slope of a Line
Parallel lines and transversals
Real Number System
Square and square roots
Congruent triangles theorem
Angles: Naming, Types, and How to Measure Them
Parallel Lines Cut by a Transversal PPT 1-9-2018.pptx
Absolute values
Linear Inequality
Radical expressions
Pairs of Angles
Coordinate plane ppt
Congruent triangles
Similar Figures
Direct and inverse proportion
1.2 Irrational Numbers ppt
2.5.5 Perpendicular and Angle Bisectors
Distance between two points
Algebraic expression
Arc length, area of a sector and segments of a circle
Slope of a Line
Ad

Similar to 1.4.1 Parallel Lines and Transversals (20)

PDF
3.2 Parallel Lines and Transversals
PDF
2.4.1 Parallel Lines and Transversals
PDF
1.3.2A Parallel Lines
PDF
Obj. 12 Parallel Lines
PPTX
Math 7 geometry 04 angles, parallel lines, and transversals - grade 7
PPTX
Parallel lines and Transversal ( Math 8 )
PPTX
Edsc 304 Teacher Lecture
PPTX
Teacher Lecture
PPTX
Edsc 304 powerpoint
PPTX
Parallelism_parallel lines cut by a transversal.ppt
PPTX
Parallel-Lines-Cut-by-a-Transversal-PPT-1-9-2018.pptx
PPTX
G8_Math_Q4-_Week_4-_Parallel-Lines-Cut-by-a-Transversal.pptx
PPTX
Geometry journal 3
PPT
Geometry unit 3.1.3.3
PPTX
Parallel-Lines-Cut-by-a-Transversal-PPT-1-9-2018.pptx
PPTX
PRESENTATION parallel and transversal lines.pptx
PPT
Geometry_Guided_Notes_Student_Copy_-Parallel-Lines-amp-TransversalsEdited.ppt
PPT
Geometry_Guided_Notes_Student_Copy_-Parallel-Lines-amp-TransversalsEdited.ppt
PPT
Parallel lines-amp-transversals edited
PPTX
LINES AND ANGLES.pptx
3.2 Parallel Lines and Transversals
2.4.1 Parallel Lines and Transversals
1.3.2A Parallel Lines
Obj. 12 Parallel Lines
Math 7 geometry 04 angles, parallel lines, and transversals - grade 7
Parallel lines and Transversal ( Math 8 )
Edsc 304 Teacher Lecture
Teacher Lecture
Edsc 304 powerpoint
Parallelism_parallel lines cut by a transversal.ppt
Parallel-Lines-Cut-by-a-Transversal-PPT-1-9-2018.pptx
G8_Math_Q4-_Week_4-_Parallel-Lines-Cut-by-a-Transversal.pptx
Geometry journal 3
Geometry unit 3.1.3.3
Parallel-Lines-Cut-by-a-Transversal-PPT-1-9-2018.pptx
PRESENTATION parallel and transversal lines.pptx
Geometry_Guided_Notes_Student_Copy_-Parallel-Lines-amp-TransversalsEdited.ppt
Geometry_Guided_Notes_Student_Copy_-Parallel-Lines-amp-TransversalsEdited.ppt
Parallel lines-amp-transversals edited
LINES AND ANGLES.pptx
Ad

More from smiller5 (20)

PDF
T7.3 The Unit Circle and Angles Presentation
PDF
T7.2 Right Triangle Trigonometry Presentation
PDF
1.3 Factoring Quadratics (Presentation).pdf
PPTX
1.3 Factoring Polynomial and Quadratic Expressions
PDF
Trigonometry 7.1 Angles (Degrees and Radians)
PDF
6.7 Exponential and Logarithmic Models
PDF
4.5 Special Segments in Triangles
PDF
1.4 Conditional Statements
PDF
1.3 Distance and Midpoint Formulas
PDF
1.5 Quadratic Equations.pdf
PDF
3.2 Graphs of Functions
PDF
3.2 Graphs of Functions
PDF
3.1 Functions
PDF
2.5 Transformations of Functions
PDF
2.2 More on Functions and Their Graphs
PDF
1.6 Other Types of Equations
PDF
1.5 Quadratic Equations (Review)
PDF
2.1 Basics of Functions and Their Graphs
PDF
9.6 Binomial Theorem
PDF
13.3 Venn Diagrams & Two-Way Tables
T7.3 The Unit Circle and Angles Presentation
T7.2 Right Triangle Trigonometry Presentation
1.3 Factoring Quadratics (Presentation).pdf
1.3 Factoring Polynomial and Quadratic Expressions
Trigonometry 7.1 Angles (Degrees and Radians)
6.7 Exponential and Logarithmic Models
4.5 Special Segments in Triangles
1.4 Conditional Statements
1.3 Distance and Midpoint Formulas
1.5 Quadratic Equations.pdf
3.2 Graphs of Functions
3.2 Graphs of Functions
3.1 Functions
2.5 Transformations of Functions
2.2 More on Functions and Their Graphs
1.6 Other Types of Equations
1.5 Quadratic Equations (Review)
2.1 Basics of Functions and Their Graphs
9.6 Binomial Theorem
13.3 Venn Diagrams & Two-Way Tables

Recently uploaded (20)

PPTX
BSCE 2 NIGHT (CHAPTER 2) just cases.pptx
PDF
The TKT Course. Modules 1, 2, 3.for self study
PPTX
PLASMA AND ITS CONSTITUENTS 123.pptx
PDF
1.Salivary gland disease.pdf 3.Bleeding and Clotting Disorders.pdf important
PPTX
Climate Change and Its Global Impact.pptx
PPTX
Reproductive system-Human anatomy and physiology
PDF
Journal of Dental Science - UDMY (2020).pdf
PDF
MICROENCAPSULATION_NDDS_BPHARMACY__SEM VII_PCI Syllabus.pdf
PDF
Myanmar Dental Journal, The Journal of the Myanmar Dental Association (2015).pdf
PPTX
4. Diagnosis and treatment planning in RPD.pptx
PDF
0520_Scheme_of_Work_(for_examination_from_2021).pdf
PPTX
pharmaceutics-1unit-1-221214121936-550b56aa.pptx
PDF
Solved Past paper of Pediatric Health Nursing PHN BS Nursing 5th Semester
PDF
Myanmar Dental Journal, The Journal of the Myanmar Dental Association (2013).pdf
PDF
Journal of Dental Science - UDMY (2022).pdf
PDF
Hospital Case Study .architecture design
PPTX
UNIT_2-__LIPIDS[1].pptx.................
PDF
Skin Care and Cosmetic Ingredients Dictionary ( PDFDrive ).pdf
PDF
Mucosal Drug Delivery system_NDDS_BPHARMACY__SEM VII_PCI Syllabus.pdf
PDF
Chevening Scholarship Application and Interview Preparation Guide
BSCE 2 NIGHT (CHAPTER 2) just cases.pptx
The TKT Course. Modules 1, 2, 3.for self study
PLASMA AND ITS CONSTITUENTS 123.pptx
1.Salivary gland disease.pdf 3.Bleeding and Clotting Disorders.pdf important
Climate Change and Its Global Impact.pptx
Reproductive system-Human anatomy and physiology
Journal of Dental Science - UDMY (2020).pdf
MICROENCAPSULATION_NDDS_BPHARMACY__SEM VII_PCI Syllabus.pdf
Myanmar Dental Journal, The Journal of the Myanmar Dental Association (2015).pdf
4. Diagnosis and treatment planning in RPD.pptx
0520_Scheme_of_Work_(for_examination_from_2021).pdf
pharmaceutics-1unit-1-221214121936-550b56aa.pptx
Solved Past paper of Pediatric Health Nursing PHN BS Nursing 5th Semester
Myanmar Dental Journal, The Journal of the Myanmar Dental Association (2013).pdf
Journal of Dental Science - UDMY (2022).pdf
Hospital Case Study .architecture design
UNIT_2-__LIPIDS[1].pptx.................
Skin Care and Cosmetic Ingredients Dictionary ( PDFDrive ).pdf
Mucosal Drug Delivery system_NDDS_BPHARMACY__SEM VII_PCI Syllabus.pdf
Chevening Scholarship Application and Interview Preparation Guide

1.4.1 Parallel Lines and Transversals

  • 1. Parallel Lines & Transversals The student is able to (I can): • Identify parallel lines, perpendicular lines, skew lines, and parallel planes • Identify – Transversals – Corresponding angles – Alternate Interior Angles – Alternate Exterior Angles – Consecutive Interior Angles
  • 2. parallelparallelparallelparallel lineslineslineslines – coplanar lines that do not intersect perpendicularperpendicularperpendicularperpendicular lineslineslineslines – two coplanar lines that intersect at right angles (90˚) m n m n f g f ⊥ g ⊥ means “perpendicular” means “parallel”
  • 3. skewskewskewskew lineslineslineslines – noncoplanar lines that do not intersect parallelparallelparallelparallel planesplanesplanesplanes – planes that do not intersect R S Plane R Plane S
  • 4. transversaltransversaltransversaltransversal – a line that intersects two coplanar lines at two different points r s t
  • 5. correspondingcorrespondingcorrespondingcorresponding anglesanglesanglesangles – angles that lie on the same side of the transversal t, on the same sides of lines r and s Example: ∠1 and ∠5 CorrespondingCorrespondingCorrespondingCorresponding anglesanglesanglesangles of parallel lines are congruent.of parallel lines are congruent.of parallel lines are congruent.of parallel lines are congruent. 87 6 5 4 3 1 2 ∠1 ≅ ∠5 ∠2 ≅ ∠6 ∠3 ≅ ∠7 ∠4 ≅ ∠8 t s r
  • 6. alternate interioralternate interioralternate interioralternate interior anglesanglesanglesangles – angles that lie on opposite sides of the transversal t, between lines r and s Example: ∠2 and ∠7 or ∠4 and ∠5 Alternate interior anglesAlternate interior anglesAlternate interior anglesAlternate interior angles of parallel lines are congruent.of parallel lines are congruent.of parallel lines are congruent.of parallel lines are congruent. r s t interior 8 7 6 5 4 3 1 2 ∠2 ≅ ∠7 ∠4 ≅ ∠5
  • 7. alternate exterioralternate exterioralternate exterioralternate exterior anglesanglesanglesangles – angles that lie on opposite sides of the transversal t, outside lines r and s Example: ∠1 and ∠8 Alternate exterior anglesAlternate exterior anglesAlternate exterior anglesAlternate exterior angles of parallel lines are congruent.of parallel lines are congruent.of parallel lines are congruent.of parallel lines are congruent. r s t exterior exterior 8 7 6 5 4 3 1 2 ∠1 ≅ ∠8 ∠4 ≅ ∠5
  • 8. consecutive interiorconsecutive interiorconsecutive interiorconsecutive interior anglesanglesanglesangles – angles that lie on the same side of the transversal t, between the lines r and s. Example: ∠3 and ∠5 ConsecutiveConsecutiveConsecutiveConsecutive interior anglesinterior anglesinterior anglesinterior angles of parallel lines areof parallel lines areof parallel lines areof parallel lines are supplementary.supplementary.supplementary.supplementary. r s t interior 87 65 43 1 2 m∠3 + m∠5 = 180˚ m∠4 + m∠6 = 180˚
  • 9. consecutiveconsecutiveconsecutiveconsecutive exterior anglesexterior anglesexterior anglesexterior angles – angles that lie on the same side of the transversal t, outside the lines r and s. Example: ∠2 and ∠8 ConsecutiveConsecutiveConsecutiveConsecutive exterior anglesexterior anglesexterior anglesexterior angles of parallel lines areof parallel lines areof parallel lines areof parallel lines are supplementary.supplementary.supplementary.supplementary. r s t interior 87 65 43 1 2 m∠1 + m∠7 = 180˚ m∠2 + m∠8 = 180˚
  • 10. 1. Find the measures of the numbered angles if m∠8 = 125˚ 2. List each angle pair corresponding angles alt. interior angles alt. exterior angles consecutive interior angles 1 2 3 8 4 5 6 7 Examples
  • 11. 1. Find the measures of the numbered angles if m∠8 = 125˚ m∠1 = 125˚; m∠2 = 55˚; m∠3 = 55˚; m∠4 = 125˚; m∠5 = 55˚; m∠6 = 55˚; m∠7 = 125˚ 2. List each angle pair corresponding angles ∠1 & ∠4; ∠2 & ∠5; ∠3 & ∠6; ∠8 & ∠7 alt. interior angles ∠3 & ∠5; ∠8 & ∠4 alt. exterior angles ∠1 & ∠7; ∠2 & ∠6 consecutive interior angles ∠3 & ∠4; ∠8 & ∠5 1 2 3 8 4 5 6 7 Examples