3004 provinglineparral
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The document discusses proving that lines are parallel using different theorems and postulates about angles and lines cut by a transversal. It introduces the converses of the corresponding angles postulate, alternate interior angles theorem, alternate exterior angles theorem, and same side interior angles theorem. It also discusses theorems about lines that are perpendicular or parallel to the same line. The objectives are to prove lines are parallel and introduce new theorems and conclusions.
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This document discusses different ways to prove that two lines are parallel using properties of parallel lines cut by a transversal. It introduces the converse theorems for corresponding angles, alternate interior angles, consecutive interior angles, and alternate exterior angles being congruent to show lines are parallel. It also presents two additional theorems: if two lines are parallel to the same line then they are parallel to each other, and if two lines are perpendicular to the same line then they are parallel to each other. The document provides example problems and homework assignments to practice these concepts.
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This document discusses angles formed when parallel lines are cut by a transversal line. It defines key terms like parallel lines, transversal, and describes angle pairs that are formed - alternate interior angles, alternate exterior angles, corresponding angles, interior angles on the same side of the transversal, and vertical angles. It notes that alternate interior angles, alternate exterior angles, and corresponding angles are congruent, while interior angles on the same side of the transversal are supplementary. Vertical angles are always equal.
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The document discusses several theorems and properties for proving when two lines are parallel, including:
1) If corresponding angles formed by a transversal intersecting two lines are congruent, then the lines are parallel.
2) If alternate interior angles or alternate exterior angles formed by a transversal are congruent, then the lines are parallel.
3) If consecutive interior angles formed by a transversal are supplementary, then the lines are parallel.
It also provides an example of using these properties to prove that if two boats sail at 45 degree angles to the constant wind, their paths will not cross since their paths are parallel.
Parallel Line Properties
If parallel lines are cut by a transversal, then:
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- Alternate exterior angles are congruent
- Interior angles on the same side of the transversal are supplementary
- Exterior angles on the same side of the transversal are supplementary
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When parallel lines are crossed by a transversal, different types of angles are formed that have specific relationships. Corresponding angles are equal, as are alternate interior angles. Interior angles on the same side of the transversal but between different parallel lines sum to 180 degrees, making them supplementary. The document defines key terms like transversal and parallel lines and provides examples of the angle relationships that occur when parallel lines are cut by a transversal.
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This document discusses properties of parallel lines cut by a transversal. It defines key terms like parallel lines, transversal, corresponding angles, alternate interior angles, and alternate exterior angles. It then presents conjectures that corresponding angles, alternate interior angles, and alternate exterior angles are congruent when two parallel lines are cut by a transversal. Examples are given to illustrate these properties and how determining the measure of one angle allows calculating the measures of all other angles formed.
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This document discusses angles formed when parallel lines are cut by a transversal line. It defines key terms like parallel lines, transversal, and describes angle pairs that are formed - alternate interior angles, alternate exterior angles, corresponding angles, interior angles on the same side of the transversal, and vertical angles. It notes that alternate interior angles, alternate exterior angles, and corresponding angles are congruent, while interior angles on the same side of the transversal are supplementary. Vertical angles are always equal.
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The document discusses several theorems and properties for proving when two lines are parallel, including:
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If parallel lines are cut by a transversal, then:
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This document discusses properties of parallel lines cut by a transversal. It defines key terms like parallel lines, transversal, corresponding angles, alternate interior angles, and alternate exterior angles. It then presents conjectures that corresponding angles, alternate interior angles, and alternate exterior angles are congruent when two parallel lines are cut by a transversal. Examples are given to illustrate these properties and how determining the measure of one angle allows calculating the measures of all other angles formed.
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The document discusses angles and parallel lines. It defines parallel lines and transversals, and explains that when a transversal intersects parallel lines, it forms eight angles that can be classified as vertical, corresponding, alternate interior, alternate exterior, adjacent, consecutive interior, and consecutive exterior angles. The document states that if two parallel lines are cut by a transversal, vertical angles, corresponding angles, alternate interior angles, and alternate exterior angles are congruent, while adjacent angles, consecutive interior angles, and consecutive exterior angles are supplementary. An example problem demonstrates finding angle measures given one is known.
Geo 3.4 proving lines parallel
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This document defines and provides examples of different types of angles and lines. It discusses intersecting and non-intersecting lines, reflex angles, adjacent angles, linear pairs of angles, vertically opposite angles, parallel lines cut by a transversal, corresponding angles, alternate interior angles, alternate exterior angles, and interior angles on the same side of a transversal. The key points are that non-intersecting lines never cross and remain the same distance apart, a reflex angle is more than 180 degrees but less than 360 degrees, and angles related to parallel lines cut by a transversal are either equal or have their sums equal 180 degrees.
5 3 finding angles
This document discusses different postulates and theorems for proving when two lines are parallel. It provides five statements for when lines are parallel based on angles formed when cut by a transversal, such as if corresponding angles are congruent. It then gives examples of applying these rules to determine if lines are parallel. The document emphasizes remembering the angle relationships that are formed when parallel lines are cut by a transversal and provides practice problems for readers to determine if lines are parallel.
Geom 3point1and2
The document discusses relationships between lines and angles formed by transversals. It defines parallel lines as coplanar lines that do not intersect, and skew lines as non-coplanar lines that do not intersect. A transversal is a line that intersects two or more coplanar lines. When a transversal crosses parallel lines, it forms corresponding, alternate interior, alternate exterior, and consecutive interior angles. There are theorems regarding perpendicular lines: if two lines intersect to form a linear pair of congruent angles, the lines are perpendicular; if the sides of two adjacent acute angles are perpendicular, the angles are complementary; and if two lines are perpendicular, they intersect to form four right angles.
Mc ds task
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The document defines and provides examples of parallel lines, perpendicular lines, skew lines, parallel planes, transversals, and the angle properties that exist when lines are cut by a transversal, including corresponding angles, alternate interior angles, alternate exterior angles, and consecutive interior angles. It states that corresponding angles, alternate interior angles, and alternate exterior angles of parallel lines cut by a transversal are congruent, while consecutive interior angles and consecutive exterior angles are supplementary.
3.2 Parallel Lines and Transversals
Identify parallel lines, perpendicular lines, skew lines, and parallel planes.
Identify transversals and angles formed by transversals.
PROVING-PROPERTIES-OF-PARALLEL-LINES-CUT-BY-TRANSVERSAL.pptx
This document discusses parallel lines cut by a transversal. It defines key terms like transversal and discusses the different angle pairs that are formed when parallel lines are cut by a transversal, including alternate interior angles, alternate exterior angles, corresponding angles, and vertical angles. The key properties are that alternate interior angles, alternate exterior angles, and corresponding angles are congruent when parallel lines are cut by a transversal.
Parallel lines Again
This document discusses properties of parallel lines cut by a transversal. It defines key terms like parallel lines, transversal, corresponding angles, alternate interior angles, and alternate exterior angles. It then presents conjectures that corresponding angles, alternate interior angles, and alternate exterior angles are congruent when two parallel lines are cut by a transversal. Examples are given to illustrate these properties and how determining the measure of one angle allows calculating the measures of all other angles formed.
Parallel lines cut by a transversal
The document defines and discusses parallel and perpendicular lines. Parallel lines are always the same distance apart and never intersect. Perpendicular lines intersect to form right angles of 90 degrees. The document provides examples of finding whether two lines are parallel or perpendicular based on their angles and relationship to a transversal or third line. It also gives examples of using corresponding, alternate interior, and alternate exterior angles to determine if lines are parallel when cut by a transversal.
2.4.1 Parallel Lines and Transversals
Identify parallel lines, perpendicular lines, skew lines, and parallel planes.
Identify corresponding angles, alternate interior angles, alternate exterior angles, and consecutive interior angles.
angle facts.ppt angle facts angle facts angle facts
This document provides information about angle facts and properties. It defines key angle terms such as acute, obtuse, right, reflex, perpendicular, and parallel lines. It describes properties of angles including: angles at a point sum to 360 degrees; opposite angles are equal; corresponding angles are equal for parallel lines with a transversal; alternate angles are equal; and interior angles sum to 180 degrees. Examples are provided to demonstrate how to use these properties to determine unknown angle measures.
Angles Formed by Parallel Lines Cut by a Transversal.pptx
When two parallel lines are cut by a transversal, several pairs of angles are formed with specific relationships. Corresponding angles are angles that have the same relative position on either side of the transversal. Alternate interior angles are interior angles on opposite sides of the transversal. Alternate exterior angles are exterior angles on opposite sides of the transversal. Consecutive interior angles are interior angles next to each other on one side of the transversal.
Pararallel lines and_transversal-2
1) The document discusses parallel and perpendicular lines as well as angles formed when lines are cut by a transversal.
2) Parallel lines never intersect and perpendicular lines intersect at right angles. A transversal is a line that intersects two or more other lines.
3) When parallel lines are cut by a transversal, 8 angles are formed. Pairs of these angles are either congruent or supplementary. Special pairs of angles, like vertical angles and corresponding angles, will be congruent.
Lines and angles For Class 7, 8, 9
This document defines and explains various angle types and angle relationships. It contains:
1) Definitions of basic angle terms like ray, line, line segment, intersecting lines, non-intersecting lines, and types of angles like acute, right, obtuse, straight, reflex, adjacent, and vertically opposite.
2) Discussions of angle relationships formed by parallel lines cut by a transversal, including corresponding angles, alternate interior angles, alternate exterior angles, and interior angles on the same side of the transversal.
3) Explanations of exterior angles of triangles and proofs related to exterior angles, vertically opposite angles, and alternate interior angles.
angles formed when two parallel lines are cut by a transversal.ppt
When two parallel lines are cut by a transversal, eight angles are formed that have specific relationships. Corresponding angles are equal, as are alternate interior angles and alternate exterior angles. If corresponding angles are equal when two lines are cut by a transversal, then the lines are parallel. Similarly, if alternate interior angles are equal, then the lines must be parallel. Understanding the angle relationships that result when parallel lines are cut by a transversal allows one to prove whether lines are parallel or determine missing angle measures.
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Math 7 geometry 04 angles, parallel lines, and transversals - grade 7
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angle facts.ppt angle facts angle facts angle facts
Angles Formed by Parallel Lines Cut by a Transversal.pptx
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angles formed when two parallel lines are cut by a transversal.ppt
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The document contains instructions and content for a geometry drill lesson. The objective is for students to discover properties of special parallelograms. The lesson includes definitions and examples of rectangles, rhombi, squares, and parallelograms. Students are asked to identify these shapes in diagrams and list their defining properties. They will also complete problems finding missing side lengths and plotting point coordinates to identify geometric objects.
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Students were instructed to place their homework from the previous Wednesday on their desk and turn in any unfinished work from the prior Friday. They were then told to copy geometry questions and self-assess their answers as a guess, unsure, or sure. The objective was to review properties of perpendicular bisectors, angle bisectors, and demonstrate what students have learned over the course of the year.
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3004 provinglineparral
- 1. GT Geom Drill #28 10/24/13 Are These Lines Parallel? a 40º 140º t b
- 5. Yes or No!! Are the converses of the corresponding angles postulate, alternate int. angles thm, alt. Ext. angles thm and same side interior angles thm true?
- 6. Yes or No!! Are the converses of the corresponding angles postulate, alternate int. angles thm, alt. Ext. angles thm and same side interior angles thm true?
- 7. OBJECTIVE To PROVE THAT LINES ARE PARALLEL.
- 8. Converse of the Corresponding Angle post If two lines are cut by a transversal such that corresponding angles are congruent, then two lines are parallel.
- 9. Converse of the Alternate Interior Angle Theorem If two lines are cut by a transversal such that alternate interior angles are congruent, then the lines are parallel.
- 10. Converse of the Same Side Interior Angle Theorem If two lines are cut by a transversal such that same side interior angles are supplementary, then the lines are parallel.
- 11. THEOREM If two lines are cut by a transversal such that alternate exterior angles are congruent, then the lines are parallel.
- 13. THEOREM If two lines are perpendicular to the same line, then the lines are parallel to each other.
- 14. NEW THEOREM If a || b and a || c, then?????????
- 15. THEOREM If two lines are parallel to the same line, then the lines are parallel to each other.
- 16. Conclusions 1) State the converses 2) If two lines are perpendicular to the same line then… 3) If two lines are parallel to the same line then...
- 18. CLASSWORK Proving Lines are Parallel #1-15
- 19. Assessment Complete ditto: “Proving Lines are Parallel II”