Share or Embed Document. Proving lines parallel worksheet answers. 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. Last but not least, if the lines are parallel, then the interior angles on the same side of the transversal are supplementary. Reward Your Curiosity. 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.
Online Student Edition. We can use the converse of these statements to prove that lines are parallel by saying that if the angles show a particular property, then the lines are parallel. This is similar to the one we just went over except now the angles are outside the pair of parallel lines. So just think of the converse as flipping the order of the statement. If the alternate exterior angles are congruent, then the lines are parallel. Proving Lines Parallel Flashcards. I would definitely recommend to my colleagues.
Amy has worked with students at all levels from those with special needs to those that are gifted. For example, if I added the angle at the bottom left of the top intersection to the angle at the top left of the bottom intersection and I got 180 degrees, then I can use this statement to prove my lines 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. Search inside document. So we look at both intersections and we look for matching angles at each corner. Unlock Your Education. Cross-Curricular Projects. Problem Solving Handbook. What are the properties that the angles must have if the lines are parallel? Through a point outside a line, there is exactly one line perpendicular ot the given line. Students also viewed. Practice 3 1 properties of parallel lines. Click to expand document information. 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. That a pair of consecutive interior angles are supplementary.
Using Converse Statements. That is all we need. What have we learned? 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. 3-5_Proving_Lines_Parallel. I feel like it's a lifeline.
Problem of the Week Cards. 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. So these angles must likewise be equal to each for parallel lines. Create your account. To begin, we know that a pair of parallel lines is a pair that never intersect and are always the same distance apart. These are the angles that are on the same corner at each intersection. All I need is for one of these to be satisfied in order to have a successful proof. 4 If 2 lines are cut by a transversal so that corresponding angles are congruent, then the lines are parallel. Don't worry, it's nothing complicated. 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. Scavenger Hunt Recording Sheet.
For parallel lines, these angles must be equal to each other. Amy has a master's degree in secondary education and has been teaching math for over 9 years.
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