Parallel LinesLines are parallel if they are always the same distance apart (called "equidistant"), and will never meet. Just remember: Show 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. It's a shame they will never meet! Try it yourself:Pairs of AnglesWhen parallel lines get crossed by another line (which is called a Transversal), you can see that many angles are the same, as in this example: These angles can be made into pairs of angles which have special names. Click on each name to see it highlighted: Now play with it here. Try dragging the points, and choosing different angle types. You can also turn "Parallel" off or on: Testing for Parallel LinesSome of those special pairs of angles can be used to test if lines really are parallel: ExamplesHotmath
In geometry, a transversal is a line that intersects two or more other (often parallel ) lines. In the figure below, line n is a transversal cutting lines l and m .
When two or more lines are cut by a transversal, the angles which occupy the same relative position are called corresponding angles . In the figure the pairs of corresponding angles are: ∠ 1 and ∠ 5 ∠ 2 and ∠ 6 ∠ 3 and ∠ 7 ∠ 4 and ∠ 8 When the lines are parallel, the corresponding angles are congruent . When two lines are cut by a transversal, the pairs of angles on one side of the transversal and inside the two lines are called the consecutive interior angles . In the above figure, the consecutive interior angles are: ∠ 3 and ∠ 6 ∠ 4 and ∠ 5 If two parallel lines are cut by a transversal, then the pairs of consecutive interior angles formed are supplementary . When two lines are cut by a transversal, the pairs of angles on either side of the transversal and inside the two lines are called the alternate interior angles . In the above figure, the alternate interior angles are: ∠ 3 and ∠ 5 ∠ 4 and ∠ 6 If two parallel lines are cut by a transversal, then the alternate interior angles formed are congruent . When two lines are cut by a transversal, the pairs of angles on either side of the transversal and outside the two lines are called the alternate exterior angles . In the above figure, the alternate exterior angles are: ∠ 2 and ∠ 8 ∠ 1 and ∠ 7 If two parallel lines are cut by a transversal, then the alternate exterior angles formed are congruent . Example 1:
In the above diagram, the lines j and k are cut by the transversal l . The angles ∠ c and ∠ e are… A. Corresponding Angles B. Consecutive Interior Angles C. Alternate Interior Angles D. Alternate Exterior Angles The angles ∠ c and ∠ e lie on either side of the transversal l and inside the two lines j and k . Therefore, they are alternate interior angles. The correct choice is C . Example 2:
In the above figure if lines A B ↔ and C D ↔ are parallel and m ∠ A X F = 140 ° then what is the measure of ∠ C Y E ? The angles ∠ A X F and ∠ C Y E lie on one side of the transversal E F ↔ and inside the two lines A B ↔ and C D ↔ . So, they are consecutive interior angles. Since the lines A B ↔ and C D ↔ are parallel, by the consecutive interior angles theorem , ∠ A X F and ∠ C Y E are supplementary. That is, m ∠ A X F + m ∠ C Y E = 180 ° . But, m ∠ A X F = 140 ° . Substitute and solve. 140 ° + m ∠ C Y E = 180 ° 140 ° + m ∠ C Y E − 140 ° = 180 ° − 140 ° m ∠ C Y E = 40 ° What are the 5 angles formed by parallel lines cut by a transversal?When any two parallel lines are cut by a transversal, there are various pairs of angles that are formed. These angles are corresponding angles, alternate interior angles, alternate exterior angles, and consecutive interior angles.
What is 2 lines cut by a transversal?If two parallel lines are cut by a transversal, then the resulting alternate exterior angles are congruent. Interior angles on the same side of the transversal: Interior angles on the same side of the transversal are also referred to as consecutive interior angles or allied angles or co-interior angles.
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