Example 1 Parallel Line Properties

Example 1 Parallel Line Properties Youtube Example 1: find out which lines are parallel to each other in the given figure. solution: all the three lines with arrows passing through them are parallel to each other, which means: a || b || c. lines with the double arrows, i.e., line d and e are transversals of lines a, b, and c, but they are parallel to each other. so, we can say that d || e. Example 8. if ∠ 1 ∘ and ∠ 8 ∘ are equal, show that ∠ 4 ∘ and ∠ 5 ∘ are equal as well. solution. the angles ∠ 1 ∘ and ∠ 8 ∘ are a pair of alternate exterior angles and are equal. recall that two lines are parallel if its pair of alternate exterior angles are equals. hence, a b ― and c d ― are parallel lines.

Parallel Lines Definition And Properties To check whether lines parallel to the same line are parallel or not, let us take an example. in the following figure, we are given that line a and line c are parallel to line b . since a || b , so ∠1 = ∠2 (corresponding angles axiom). Example 1: determine if the lines p, q, and r are parallel. solution: here, the pair of corresponding angles are equal, that is 65° and the pair of alternate exterior angles are equal, that is 115°. therefore, with the angles property of parallel lines, we can conclude that the lines p, q, and r are parallel. example 2: l and m are two. Parallel lines are seen in many common 2d shapes. for example, each side of a square is made of a line segment that is part of a line. the opposite sides of a square are parallel. there are also many examples of parallel lines in real life. for example, the lines that pass by the sides of a table top are parallel. Pairs of angles. when 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.