a. Line segment: A line with definite end points is called a line segment. It is denoted as AB¯¯¯¯¯¯¯¯AB¯.
b. Line: A line segment when extended infinitely from both ends, we get a line. It is denoted as AB←→AB↔.
c. Ray: A line with one endpoint is called a ray. It is denoted by AB−→−AB→.
d. Angle: When two lines or line segments intersect or meet at a common point, an angle is formed. For example, in the figure below, we can see the angles formed by the lines PQ←→PQ↔ and RS←→RS↔ are ∠POS,∠SOQ,∠QOR∠POS,∠SOQ,∠QOR and ∠ROP∠ROP.
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Related Angles:
a. Complementary angles: Two angles having the sum of their measures equal to 90∘90∘ are called complementary angles. When two angles are complementary, one angle is called the complement of another angle. An example has been shown below.
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b. Supplementary angles: Two angles having the sum of their measures equal to 180∘180∘ are called supplementary angles. When two angles are complementary, one angle is called the supplement of another angle. An example has been shown below.
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c. Adjacent angle: The pair of angles present next to each other such that they have a common vertex, one common arm and the non-common arm lies on either side of the common arm. In the diagram given below, ∠1∠1 and ∠2∠2 are adjacent angles.
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d. Linear pair: The adjacent angles who are supplementary to each other are called the linear pairs. The non-common arms of these angles are rays moving in opposite directions. In the diagram given below, ∠1∠1 and ∠2∠2 are linear pair angles.
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e. Vertically opposite angles: Two lines that cross each other, four angles are formed as shown in the diagram below.
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Here, ∠1&∠3∠1&∠3 and ∠2&∠4∠2&∠4 are vertically opposite to each other.
Pairs of Lines:
a. Intersecting lines: two lines when crosses each other at only one point, then they are called the intersecting lines and that point is called the point intersection. As in the diagram below, ll and mmare intersecting lines with their point of intersection AA.
b. Transversal: When two or more distinct lines are intersected by a common line, then that line is called a transversal. As in the figure below, lines ll and mm are intersected by a common line pp which is the transversal. This transversion creates eight angles.
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The relation between the eight angles have been tabulated below.
| Interior angles | ∠3,∠4,∠5,∠6∠3,∠4,∠5,∠6 |
| Exterior angles | ∠1,∠2,∠7,∠8∠1,∠2,∠7,∠8 |
| Pairs of corresponding angles | ∠1&∠5,∠2&∠6,∠3&∠7,∠4&∠8∠1&∠5,∠2&∠6,∠3&∠7,∠4&∠8 |
| Pairs of alternate interior angles | ∠3&∠6,∠4&∠5∠3&∠6,∠4&∠5 |
| Pairs of alternate exterior angles | ∠1&∠8,∠2&∠7∠1&∠8,∠2&∠7 |
| Pairs of interior angles on the same side of transversal | ∠3&∠5,∠4&∠6∠3&∠5,∠4&∠6 |
Traversal of Parallel Lines:
When a pair of parallel lines ll and mm are intersected by a line tt, then following properties can be observed.
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1. Each pair of corresponding angles are equal. e.g., ∠7=∠8,∠1=∠2∠7=∠8,∠1=∠2, etc.
2. Each pair of alternate interior angles are equal. e.g., ∠3=∠8,∠1=∠6∠3=∠8,∠1=∠6, etc.
3. Each pair of interior angles on the same side of the transversal are supplementary to each other. e.g., ∠1+∠8=180∘∠1+∠8=180∘, etc
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