So if one angle was at the top left corner at one intersection, the corresponding angle at the other intersection will also be at the top left. You will see that the transversal produces two intersections, one for each line. 'Interior' means that both angles are between the two lines that are parallel. Proving Lines Parallel Section 3-5. Converse of the Consecutive Interior Angles Theorem If two lines are cut by a transversal such that a pair of consecutive interior angles are supplementary, then the two lines are parallel. Cross-Curricular Projects. Proving Lines Parallel Flashcards. For parallel lines, these angles must be equal to each other. 576648e32a3d8b82ca71961b7a986505. 0% found this document not useful, Mark this document as not useful. Students also viewed.
Jezreel Jezz David Baculna. Online Student Edition. So, if my angle at the top right corner of the top intersection is equal to the angle at the bottom left corner of the bottom intersection, then by means of this statement I can say that the lines are parallel. We have four original statements we can make. 3 5 practice proving lines parallel structure. This transversal creates eight angles that we can compare with each other to prove our lines parallel. That both lines are parallel to a 3 rd line.
Joke Time How do you know when it's raining cats and dogs? Sets found in the same folder. This line creates eight different angles that we can compare with each other. Where x is the horizontal distance (in yards) traveled by the football and y is the corresponding height (in feet) of the football. We know that in order to prove a pair of parallel lines, lines that never intersect and are always the same distance apart, are indeed parallel, we need a transversal, which is a line that intersects two other lines. Proving lines parallel practice. So, for example, if we found that the angle located at the bottom-left corner at the top intersection is equal to the angle at the top-right corner at the bottom intersection, then we can prove that the lines are parallel using this statement. Here, the angles are the ones between the two lines that are parallel, but both angles are not on the same side of the transversal.
Problem of the Week Cards. © © All Rights Reserved. Because it couldn't find a date. You're Reading a Free Preview. Problem Solving Handbook.
To prove any pair of lines is parallel, all you need is to satisfy one of the above. It's like a teacher waved a magic wand and did the work for me. That is all we need. Share this document. So if you're still picturing the tracks on a roller coaster ride, now add in a straight line that cuts across the tracks. Other sets by this creator.
If the alternate exterior angles are congruent, then the lines are parallel. Last but not least, if the lines are parallel, then the interior angles on the same side of the transversal are supplementary. Document Information. Terms in this set (11). We started with 'If this, then that, ' and we ended up with 'If that, then this. Proving lines parallel answers. ' The path of the kicked football can be modeled by the graph of. Will the football pass over the goal post that is 10 feet above the ground and 45 yards away? Everything you want to read. See for yourself why 30 million people use. A football player is attempting a field goal. When the lines are indeed parallel, the angles have four different properties.
So, a corresponding pair of angles will both be at the same corner at their respective intersections. Now, with parallel lines, we have our original statements that tell us when lines are parallel. If any of these properties are met, then we can say that the lines are parallel. So, if the interior angles on either side of the transversal add up to 180 degrees, then I can use this statement to prove the lines are parallel.
If we had a statement such as 'If a square is a rectangle, then a circle is an oval, ' then its converse would just be the same statement but in reverse order, like this: 'If a circle is an oval, then a square is a rectangle. ' But in order for the statements to work, for us to be able to prove the lines are parallel, we need a transversal, or a line that cuts across two lines. You will see that it forms eight different angles. So just think of the converse as flipping the order of the statement.
What are the properties that the angles must have if the lines are parallel? To use this statement to prove parallel lines, all we need is to find one pair of corresponding angles that are congruent. Save 3-5_Proving_Lines_Parallel For Later. Report this Document. In a plane, if 2 lines are perpendicular to the same line, then they are parallel. Original Title: Full description. Resources created by teachers for teachers. These properties are: - The corresponding angles, the angles located the same corner at each intersection, are congruent, - The alternate interior angles, the angles inside the pair of lines but on either side of the transversal, are congruent, - The alternate exterior angles, the angles outside the pair of lines but on either side of the transversal, are congruent, and.
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Unlock Your Education. Click to expand document information. Register to view this lesson. California Standards Practice (STP). So we look at both intersections and we look for matching angles at each corner. 12. are not shown in this preview. Reward Your Curiosity. The resource you requested requires you to enter a username and password below: A plane, show that both lines are perpendicular to a 3 rd line.
The interior angles on the same side of the transversal are supplementary. Did you find this document useful? Prove parallel lines using converse statements by creating a transversal line. That a pair of consecutive interior angles are supplementary. Share or Embed Document. Lines e and f are parallel because their same side exterior angles are congruent. Recent flashcard sets.
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