The second definition is the one which Euclid adopted and it is pretty common in textbooks. The first definition is mathematically sound but it is also the most awkward as it describes a critical property of parallel lines and is most appropriately seen as a theorem rather than a definition. The sum of all the angles around a point is always 360 degrees.įor example, Sum of angles (∠1, ∠2, and ∠3) around point O is 360 degrees.The goal of this task is to critically analyze several possible definitions for parallel lines. The sum of all the angles on one side of a straight line is always 180 degrees.įor example, The sum of ∠1, ∠2, and ∠3 is 180 degrees. Properties of Angles Sum of angles on one side of a straight line Let us now learn about a few properties of angles. So, we have discussed all the type of angles. Note: If a transversal line intersects two parallel lines, then the corresponding angles, alternate interior angles, and alternate exterior angles are equal. (∠1, ∠7) and (∠4, ∠6) are alternate exterior angles.Two exterior angles that are present on the opposite side of the transversal line are called alternate exterior angles. (∠2, ∠8) and (∠3, ∠5) are alternate interior angles.Two interior angles, present on the opposite side of a transversal line, are called alternate interior angles. (∠4, ∠8), (∠3, ∠7), (∠1, ∠5), and (∠2, ∠6) are 4 pairs of corresponding angles Alternate interior angles Two angles are said to be corresponding angles if they lie on the same side of the transversal line such that: And, ∠1, ∠4, ∠6, and ∠7 are exterior angles.
∠2, ∠3, ∠5, and ∠8 are interior angles. And, exterior angles are the ones that are not present inside this region. Interior angles are the ones that are present inside the region between two lines. Other types of Angles Interior and Exterior Angles Similarly, we get several other types of angles. Now, there are several special pairs of angles that are obtained from this diagram.įor example: If you notice (∠1, ∠3), (∠2, ∠4), (∠5, ∠7), and (∠6, ∠8) are all vertically opposite angles. When a transversal line intersects two lines, then eight angles are formed as shown. We represent an angle by the symbol ∠.Īn angle involves two legs and one common vertex at which two lines meet.įor example, ∠AOD is formed when lines AB and CD intersect with each other.Īlso, ∠AOD is formed between the leg AO and OD, so we include A, O, and D while naming the angle.ĭo you know that the position of leg points does not matter as long as the common vertex is the middle letter in the angle name Measurement of an Angle Watch this video to know more: Angle – What is it?Īn angle is formed when two lines intersect each other. Our xPERT not only curates the most optimized learning path but also tracks your improvement, ensuring that you get to your target Quant score quickly and reliably. Start your journey of getting a Q50-51 on the GMAT with e-GMAT’s AI-driven online preparation course. Scoring a Q50-51 on the GMAT helps you get a 700+ GMAT score. Next, we take a look at angles and their properties. Transversal LineĪ transversal line cuts two or more lines at distinct points.įor example, Line L 3 is the transversal line in the below diagram. Two lines are intersecting lines if they meet each other at a common point.įor example, L 1 and L 2 are intersecting lines in the below diagram Parallel LinesĪ pair of lines are parallel if they never intersect.įor example, L 1, L 2, and L 3 are parallel lines in the below diagram. In a plane, there can be many lines or line segments.Īnd, these lines can be divided into a few types based on the relative positioning of a line with another line. 
Definition of a Line SegmentĪ line segment is a segment of a line, or in other words, we can say that a line segment is a line with two endpoints.įor example, The diagram shows a line L and one segment of this line is AB. Application of Lines and Angles Properties in QuestionsĪ line does not have any endpoints.Angles formed between two intersecting lines.
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