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- Congruent lines are identical in length and shape, whereas parallel lines are lines that never meet and have the same slope.
www.intmath.com/functions-and-graphs/congruent-lines.php
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: Parallel lines also point in the same direction. Parallel lines have so much in common.
- Alternate Interior Angles
To help you remember: the angle pairs are on Alternate sides...
- Corresponding Angles
When two lines are crossed by another line (called the...
- Vertical Angles
(in fact they are congruent angles) Have a play with them...
- 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...
- 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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Jan 16, 2024 · To figure out if 2 lines are parallel, compare their slopes. You can find the slope of a line by picking 2 points with XY coordinates, then put those coordinates into the formula Y2 minus Y1 divided by X2 minus X1. Calculate the slope of both lines. If they are the same, then the lines are parallel.
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Mar 26, 2016 · Proving that angles are congruent: If a transversal intersects two parallel lines, then the following angles are congruent (refer to the above figure): Alternate interior angles: The pair of angles 3 and 6 (as well as 4 and 5) are alternate interior angles.
Jan 11, 2023 · If a transversal cuts across two lines to form two congruent, corresponding angles, then the two lines are parallel. To know if we have two corresponding angles that are congruent, we need to know what corresponding angles are.
There are a few ways to tell when two lines are parallel: Check their slopes and y-intercepts: if the two lines have the same slope, but different y-intercepts, then they are parallel. Check the distance between them: if two lines always have the same distance between them, then they are parallel.
Learn what it means for two figures to be congruent, and how to determine whether two figures are congruent or not. Use this immensely important concept to prove various geometric theorems about triangles and parallelograms.
