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Types of lines:
Intersecting lines:
Two lines are intersecting lines if they meet each other at a common point.
For example: L1 and L2 are intersecting lines in the diagram that is shown below.
Parallel lines:
A pair of lines are said to be parallel if they never intersect.
For example: L1, L2, and L3 are parallel lines in the diagram that is shown below.
Transversal line:
A line that intersects two or more lines at distinct points is called a transversal line.
For example: Line L3 is the transversal line in the diagram that is shown below.
Angle:
An angle is formed when two lines intersect with each other. We represent an angle by the symbol ∠.
An angle involves two legs and one common vertex at which two lines meet.
For example: ∠AOD is formed when lines AB and CD intersect with each other.
Also, ∠AOD is formed between the legs AO and OD. So, we include A, O, and D while naming the angle.https://grdp.co/cdn-cgi/image/width=500,height=500,quality=50,f=auto/https://gs-post-images.grdp.co/2022/7/image-39-img1658404995195-94.png-rs-high-webp.png
The angle is measured in degrees or radians.
An angle can measure from zero (0) degrees to 360 degrees.
And, based on the measurement of an angle, they are divided into four types.
1. Acute angle:
When the measurement of the angle is between 0 degrees and 90 degrees, the angle is known as an acute angle.
2. Right angle:
When the measurement of the angle is exactly 90 degrees, the angle is known as a right angle.
Note: If there is a right angle between two lines, then the two lines are said to be perpendicular to each other.
3. Obtuse angle:
When the measurement of the angle is between 90 degrees and 180 degrees, the angle is known as an obtuse angle.
4. Reflex angle:
When the measurement of the angle is between 180 degrees and 360 degrees, the angle is known as a reflex angle.
Angles formed between two intersecting lines:
Vertically opposite angles:
When two lines intersect each other, 4 angles are formed.
And the angles that are opposite to each other at the intersection point are known as vertically opposite angles.
Vertically opposite angles are always equal.
Angles formed by a transversal line:
When a transversal line intersects two lines, eight angles are formed as shown in the figure that is given below.
Now, there are several special pairs of angles that are obtained from this diagram.
- For example: You can observe that (∠1, ∠3), (∠2, ∠4), (∠5, ∠7), and (∠6, ∠8) are all vertically opposite angles.
Interior and exterior angles:
Interior angles are the ones that are present inside the region between two lines, and exterior angles are the ones that are not present inside this region.
For example: ∠2, ∠3, ∠5, and ∠8 are interior angles. And ∠1, ∠4, ∠6, and ∠7 are exterior angles.
Corresponding angles:
Two angles are said to be corresponding angles if they lie on the same side of the transversal line such that one angle is an interior angle and another is an exterior angle.
Alternate interior angles:
Two interior angles that are present on the opposite side of a transversal line are called alternate interior angles.
Alternate exterior angles:
Two exterior angles that are present on the opposite side of a transversal line are called alternate exterior angles.
Properties of angles:
- The sum of all the angles on one side of a straight line is always 180 degrees.
- The sum of all the angles around a point is always 360 degrees.
Some important points:
- When two angles, A and B, are complementary, the sum of A and B is 90°.
- When two angles, A and B, are supplementary, the sum of A and B is 180°.
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