Properties of parallel lines gsp5 answers

в€ FGD + в€ DGH = 180 0 вЂ¦вЂ¦.(angles are in linear pair) EH is a transversal.What is the measure of angle AFG? Solved ExamplesД®xample 1: AB and CD are parallel lines. These state the parallel lines and its properties. If two parallel lines are intersected by a transversal then the pair of interior angles on the same side of the transversal are supplementary.Д¬onversely, if the pair of co-interior angles are supplementary then the given lines are parallel to each other. I.e If two lines which are parallel are intersected by a transversal then the pair of alternate interior angles are equal.Д¬onversely, if the pair of alternate interior angles are equal then the given lines are parallel to each other. If two parallel lines are intersected by a transversal then the pair of alternate interior angles are equal. The below theorem can be proved if we assume that one of them always holds good.Д«y considering the corresponding angle axiom we can prove the below theorems. If two parallel lines are intersected by a transversal, then each pair of corresponding angles are equal.Д¬onversely, if pairs of corresponding angles are equal, then the given lines are parallel to each other. The following are the axioms and theorems for the parallel lines. Parallel Lines Axioms and TheoremД¬onsider line a|| b and l is the transversal. Now, let us study the relations between the angles of the pairs when the two lines are parallel to each other and under the condition for parallel lines. Two pairs of interior angles on the same side of the transversal are called pairs of consecutive interior angles. Two angles on the same side of a transversal are known as the corresponding angles if both lie above the two lines or below the two lines. When a transversal intersects two lines it forms some pair of angles they are as follows в€ 3, в€ 4, в€ 5, and в€ 6 are the interior angles because they are inside the lines. в€ 1, в€ 2, в€ 7, and в€ 8 are the exterior angles because they are outside the lines. The transversal intersects two lines in two points and makes 4 angles at each intersecting point. In the figure below the red line indicates the transversal. TransversalДЄ line that intersects two or more lines at different points, is called a transversal of the given lines. A line that intersects two or more lines at different points is called a transversal. The lines that are not parallel to each other and if they cross each other they are called intersecting lines. One and only one parallel line can be drawn parallel to a given line through a given point which is not lying on the given line. Two lines in the same plane and perpendicular to the same line are parallel to each other.

If two lines are parallel to the same line, then all the three lines are parallel to each other. The perpendicular distance between two parallel lines is equal everywhere. Some of the important properties of parallel lines are: Some of the condition for parallel lines are discussed below Properties of Parallel Lines Parallel lines are indicated with a pair of vertical pipes between the line names like line m is parallel to line n written as m || nДЄn easy way to remember parallel lines is to assume вЂњequal to (=)вЂќ sign. The symbol for parallel lines is || and it is called вЂparallel toвЂ™. The perpendicular distance between the two parallel lines always remains the same. When the two straight lines on the same plane do not intersect, they are called parallel lines. Let us study parallel lines and its properties. Two lines are parallel, if they are drawn in the same plane. We come across parallel lines in daily life, we see parallel lines in railway tracks, zebra crossing, stairs, walls, window linings, lines in notebook pages, etc. If the distance between two lines is always the same, the lines are said as parallel lines.

Properties of parallel lines gsp5 answers