Two lines that are stretched into infinity and still never intersect are called coplanar lines and are said to be parallel lines. The symbol for "parallel to" is //. Show
If we have two lines (they don't have to be parallel) and have a third line that crosses them as in the figure below - the crossing line is called a transversal:  In the following figure: If we draw to parallel lines and then draw a line transversal through them we will get eight different angles. The eight angles will together form four pairs of corresponding angles. Angles F and B in the figure above constitutes one of the pairs. Corresponding angles are congruent if the two lines are parallel. All angles that have the same position with regards to the parallel lines and the transversal are corresponding pairs. Angles that are in the area between the parallel lines like angle H and C above are called interior angles whereas the angles that are on the outside of the two parallel lines like D and G are called exterior angles. Angles that are on the opposite sides of the transversal are called alternate angles e.g. H and B. Angles that share the same vertex and have a common ray, like angles G and F or C and B in the figure above are called adjacent angles. As in this case where the adjacent angles are formed by two lines intersecting we will get two pairs of adjacent angles (G + F and H + E) that are both supplementary. Two angles that are opposite each other as D and B in the figure above are called vertical angles. Vertical angles are always congruent. $$\angle A\; \angle F\; \angle G\; \angle D\;are\; exterior\; angles\\ \angle B\; \angle E\; \angle H\; \angle C\;are\; interior\; angles\\ \angle B\;and\; \angle E,\; \angle H\;and\; \angle C\;are\; consecutive\; interior\; angles\\ \angle A\;and\; \angle G,\; \angle F\;and\; \angle D\;are\; alternate\; exterior\; angles\\ \angle E\;and\; \angle C,\; \angle H\;and\; \angle B\;are\; alternate\;interior\; angles\\ \left.\begin{matrix} \angle A\;and\; \angle E,\; \angle C\;and\; \angle G\\ \angle D\;and\; \angle H,\; \angle F\;and\; \angle B\\ \end{matrix}\right\} \;are\; corresponding\; angles$$ Two lines are perpendicular if they intersect in a right angle. The axes of a coordinate plane is an example of two perpendicular lines. In algebra 2 we have learnt how to find the slope of a line. Two parallel lines have always the same slope and two lines are perpendicular if the product of their slope is -1. A line that intersects two or more other lines is called a transversal. When a transversal intersects two parallel lines, it creates eight angles that include corresponding angles, alternate interior angles, alternate exterior angles, and same-side interior angles. In this eighth-grade geometry worksheet, students will practice identifying these different types of angle pairs using given diagrams. Students will then use those angle relationships to find missing angle measures on two other diagrams and explain how they found the missing angle measures. For more practice with parallel lines cut by a transversal, complete the Transversals of Parallel Lines worksheet. You’ll gain experience classifying line types, identifying angle relationships, and finally using that knowledge to solve problems for missing angles. Let jump in! What Are Parallel Lines?What comes to mind when you think of parallel lines? Is it the definition, which states that parallel lines are coplanar and never intersect because they are the same distance apart? Or perhaps you envision two lines that have the same slope and different y-intercepts as we learned in Algebra? Or maybe it’s just a visual image like a railroad track or a picket fence. Parallel Lines Examples What Is A Transversal?A transversal is a line that intersects two or more coplanar lines, each at a different point. What this means is that, two lines are intersected by a third line, and in so doing, creates six angle-pair relationships as demonstrated below:
Transversal Line Example Parallel Lines and Transversals PostulatesParallel lines and transversals are very important to the study of geometry because they enable us to define congruent angle pair relationships. How? Well, when two parallel lines are cut by a transversal (i.e., get crossed by a third line), then not only do we notice the vertical angles and linear pairs that are subsequently formed, but the following angle pair relationships are created as well:
And knowing how to identify these angle pair relationships is crucial for proving two lines are parallel, as Study.Com accurately states. In the video below, you’ll discover that if two lines are parallel and are cut by a transversal, then all pairs of corresponding angles are congruent (i.e., same measure), all pairs of alternate exterior angles are congruent, all pairs of alternate interior angles are congruent, and same side interior angles are supplementary! Transversal AnglesCorresponding Angles∠1 is congruent to ∠5 Corresponding Angles Alternate Exterior Angles∠1 is congruent to ∠8 Alternate Exterior Angles Alternate Interior Angles∠3 is congruent to ∠5 Alternate Interior Angles Same Side Interior Angles∠3 and ∠6 are supplementary Same Side Interior Angles Wow! In the following video, you’ll learn all about classifying lines as parallel, intersecting, or skew. Then you’ll learn how to identify transversal lines and angle pair relationships. Next, you’ll use your knowledge of parallel lines to determine the measure of angles. And lastly, you’ll write two-column proofs given parallel lines. How do you answer parallel lines cut by a transversal?If two parallel lines are cut by a transversal, each pair of alternate interior angles are equal. If two parallel lines are cut by a transversal, then each pair of interior angles on the same side of the transversal are supplementary, i.e. they add up to 180 degrees.
When two parallel lines are cut by transversal?If two parallel lines are cut by a transversal, then, Alternate Exterior Angles are congruent. If two parallel lines are cut by a transversal, then corresponding angles are congruent. Two lines cut by a transversal are parallel IF AND ONLY IF corresponding angles are congruent.
How do you solve two parallel lines crossed by a transversal?If a transversal intersects two parallel lines, then each pair of interior angles on the same side of the transversal is supplementary, i.e. they add up to 180°. When two lines intersect each other, then the opposite angles, formed due to intersection, are called vertical angles or vertically opposite angles.
How many angles do 2 parallel lines cut by a transversal create?If we draw to parallel lines and then draw a line transversal through them we will get eight different angles. The eight angles will together form four pairs of corresponding angles. Angles F and B in the figure above constitutes one of the pairs. Corresponding angles are congruent if the two lines are parallel.
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Two parallel lines cut by a transversal answer key
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