Hi Friends! In this online tutors homework help session we will talk about parallel lines cut by a transversal. Let us consider two lines which are at equidistance from each other at any point of observation. It means that when we draw a perpendicular at any point from one line to another, we observe that all perpendiculars are of equal length. In this unit we will discuss about the topic parallel lines cut by a transversal. If two parallel lines are intersected by a line which intersect both the lines, then it is called a transversal. To understand parallel lines cut by a transversal definition, we say that a transversal is the line which meets two parallel lines at some point. So a transversal has a point of intersection on both the parallel lines.
Let us consider two parallel lines say ‘l’ and ‘m’. Let ‘n’ be the transversal drawn on the two parallel lines. Now the following conditions are satisfied:
1. Since we have l|| m, then the corresponding angles formed by the transversal are equal. These types of angles are four in pairs.
2. The pair of interior opposite angles is supplementary. These angles are 2 in pairs.
3. The pair of interior alternate angles so formed is also equal. These angles are 2 in pair.
4. Also exterior alternate angles are equal. They are also 2 in numbers.
Now keeping these qualities in mind, if one of the angles among all the angles is known, we can find rest of the angles so formed. To find these angles we may use the property of vertical opposite angles are equal, corresponding angles of the two parallel lines, cut by a transversal are equal, Linear pair and the property of alternate angles.
Besides this we come across the problems where we are given some of the measures of the angles (also see Complementary Angles Definition) and we need to find if the two lines which are cut by the transversal are equal or not. This discussion will help students of grade XII to understand the concept of parallel lines cut by a transversal.
Let us consider two parallel lines say ‘l’ and ‘m’. Let ‘n’ be the transversal drawn on the two parallel lines. Now the following conditions are satisfied:
1. Since we have l|| m, then the corresponding angles formed by the transversal are equal. These types of angles are four in pairs.
2. The pair of interior opposite angles is supplementary. These angles are 2 in pairs.
3. The pair of interior alternate angles so formed is also equal. These angles are 2 in pair.
4. Also exterior alternate angles are equal. They are also 2 in numbers.
Now keeping these qualities in mind, if one of the angles among all the angles is known, we can find rest of the angles so formed. To find these angles we may use the property of vertical opposite angles are equal, corresponding angles of the two parallel lines, cut by a transversal are equal, Linear pair and the property of alternate angles.
Besides this we come across the problems where we are given some of the measures of the angles (also see Complementary Angles Definition) and we need to find if the two lines which are cut by the transversal are equal or not. This discussion will help students of grade XII to understand the concept of parallel lines cut by a transversal.
In upcoming posts we will discuss about triangle inequality theorem and Measures of central tendency. Visit our website for information on biology syllabus for class 10 ICSE
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