Become a member and start learning a Member. Proving Lines Parallel Section 3-5. Remember what converse statements are. Don't worry, it's nothing complicated. Is this content inappropriate? Problem Solving Handbook. That a pair of alternate exterior angles are congruent.
Joke Time How do you know when it's raining cats and dogs? You will see that the transversal produces two intersections, one for each line. You will see that it forms eight different angles.
If the alternate exterior angles are congruent, then the lines are parallel. For example, if we found that the top-right corner at each intersection is equal, then we can say that the lines are parallel using this statement. 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. Where x is the horizontal distance (in yards) traveled by the football and y is the corresponding height (in feet) of the football. All we need here is also just one pair of alternate interior angles to show that our lines are parallel. 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. Proving lines are parallel. Recent flashcard sets. We have four original statements we can make. Along with parallel lines, we are also dealing with converse statements. All I need is for one of these to be satisfied in order to have a successful proof. Did you find this document useful? 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. Sets found in the same folder. Share this document.
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. 'Interior' means that both angles are between the two lines that are parallel. 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. The process of studying this video lesson could allow you to: - Illustrate parallel lines. Scavenger Hunt Recording Sheet. 3 5 practice proving lines parallel quiz. For parallel lines, these angles must be equal to each other. You are on page 1. of 13. These are the angles that are on the same corner at each intersection. What are the properties that the angles must have if the lines are parallel? You need this to prove parallel lines because you need the angles it forms because it's the properties of the angles that either make or break a pair of parallel lines. To unlock this lesson you must be a Member. To begin, we know that a pair of parallel lines is a pair that never intersect and are always the same distance apart.
To prove any pair of lines is parallel, all you need is to satisfy one of the above. 12. are not shown in this preview. Now let's look at how our converse statements will look like and how we can use it with the angles that are formed by our transversal. Share with Email, opens mail client.
4 If 2 lines are cut by a transversal so that corresponding angles are congruent, then the lines are parallel. This is what parallel lines are about. Search inside document. Using Converse Statements to Prove Lines Are Parallel - Video & Lesson Transcript | Study.com. Students also viewed. Parallel Lines Statements. 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. ' 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.
Amy has a master's degree in secondary education and has been teaching math for over 9 years. These must add up to 180 degrees. In a plane, if 2 lines are perpendicular to the same line, then they are parallel. Theorem 2 lines parallel to a 3 rd line are parallel to each other. 3 5 practice proving lines parallel programming. So if you're still picturing the tracks on a roller coaster ride, now add in a straight line that cuts across the tracks. This transversal creates eight angles that we can compare with each other to prove our lines parallel. When the lines are indeed parallel, the angles have four different properties. Will the football pass over the goal post that is 10 feet above the ground and 45 yards away? To use this statement to prove parallel lines, all we need is to find one pair of corresponding angles that are congruent. This is similar to the one we just went over except now the angles are outside the pair of parallel lines. So we look at both intersections and we look for matching angles at each corner.
Create your account. Share or Embed Document. Reward Your Curiosity. If the lines are parallel, then the alternate exterior angles are congruent. © © All Rights Reserved. This line creates eight different angles that we can compare with each other. Unlock Your Education.
Problem of the Week Cards. Think of the tracks on a roller coaster ride. If any of these properties are met, then we can say that the lines are parallel. Cross-Curricular Projects.
Buy the Full Version. Everything you want to read. A football player is attempting a field goal. Why did the apple go out with a fig? Lines e and f are parallel because their same side exterior angles are congruent. Do you see how they never intersect each other and are always the same distance apart? That a pair of consecutive interior angles are supplementary. The word 'alternate' means that you will have one angle on one side of the transversal and the other angle on the other side of the transversal. When you step in a poodle! Register to view this lesson. 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.
576648e32a3d8b82ca71961b7a986505. 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. Online Student Edition. Last but not least, if the lines are parallel, then the interior angles on the same side of the transversal are supplementary. The interior angles on the same side of the transversal are supplementary. Chapter Readiness Quiz. Through a point outside a line, there is exactly one line perpendicular ot the given line. The resource you requested requires you to enter a username and password below: Document Information. Other Calculator Keystrokes. This is your transversal. Using Converse Statements. Report this Document. Other sets by this creator.
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