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Parallel Lines, and Pairs of Angles Parallel Lines. Lines are parallel if they are always the same distance apart (called "equidistant"), and will never meet. Just remember: Always the same distance apart and never touching. The red line is parallel to the blue line in each of these examples:
- Alternate Interior Angles
To help you remember: the angle pairs are on Alternate sides...
- Corresponding Angles
When the two lines being crossed are Parallel Lines the...
- Vertical Angles
Notice how the 4 angles are actually two pairs of "vertical...
- Alternate Exterior Angles
To help you remember: the angle pairs are on Alternate sides...
- Line in Geometry
Ray. When it has just one end it is called a "Ray". This is...
- Consecutive Interior Angles
To help you remember: the angle pairs are Consecutive (they...
- Congruent Angles
Congruent Angles Congruent Angles have the same angle (in...
- Parallel Lines Definition
Lines on a plane that never meet. They are always the same...
- Alternate Interior Angles
- Teaching Strategies on How to Prove Lines Are Parallel
- Activities For Proving Lines Are Parallel
- Before You Leave…
Review Logic in Geometry and Proof
In your lesson on how to prove lines are parallel, students will need to be mathematically fluent in building an argument. They should already know how to justify their statements by relying on logic. That’s why it’s advisable to briefly review earlier knowledge on logic in geometry. You can check out our articleon this topic for more guidelines and activities, as well as this article on proving theorems in geometry which includes a step-by-step introduction on statements and reasons used in...
Ways to Prove Lines Are Parallel
For starters, draw two parallel lines on the whiteboard, cut by a transversal. Remind students that a line that cuts across another line is called a transversal. If the line cuts across parallel lines, the transversal creates many angles that are the same. Remind students that when a transversal cuts across two parallel lines, it creates 8 angles, which we can sort out in angle pairs. Point out that we will use our knowledge on these angle pairs and their theorems (i.e. the converse of their...
Additional Resources:
If you have the technical means in your classroom, you may also decide to complement your lesson on how to prove lines are parallel with multimedia material, such as videos. This free geometry videois a great way to do so. The video contains simple instructions and examples on the converse of the alternate interior angles theorem, converse of the corresponding angles theorem, converse of the same-side interior angles postulate, as well as the converse of the alternate exterior angles theorem....
Pair Work
This is a simple activity that will help students reinforce their skills at proving lines are parallel. Introduce this activity after you’ve familiarized students with the converse of the theorems and postulates that we use in proving lines are parallel. Prepare a worksheet with several math problems on how to prove lines are parallel. For instance, students are asked to prove the converse of the alternate exterior angles theorem using the two-column proof method. Include a drawing and which...
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If two lines are cut by a transversal and the alternate exterior angles are congruent, the lines are parallel. To show that congruent exterior angles will also prove the lines parallel, we will establish a connection between the exterior angles and angles 1 and 2, which are inside the triangles.
If 2 lines are cut by a transversal and the alternate interior angles are congruent, the lines are parallel. 5. Parallel Postulate: Through a point not on a given line, only one line can be drawn parallel to the given line.
Mar 26, 2016 · Proving that lines are parallel: All these theorems work in reverse. You can use the following theorems to prove that lines are parallel. That is, two lines are parallel if they’re cut by a transversal such that. Two corresponding angles are congruent. Two alternate interior angles are congruent. Two alternate exterior angles are congruent.
Parallel Lines: Theorem. The lines which are parallel to the same line are parallel to each other as well. This property holds good for more than 2 lines also. Example. In the following figure, m, n, and l are parallel lines. And AB is parallel to CD. Find the value of angle x using the given angles. Solution:
People also ask
How do you know if a line is parallel or congruent?
Which lines are parallel to the same line?
What if 3 is congruent to 5?
Are all four angle types congruent?
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What happens when a parallel line is crossed by a transversal?
If two lines are cut by a transversal and the alternate exterior angles are congruent, the lines are parallel. Corresponding Angles: The name does not clearly describe the "location" of these angles.
