|Conic Section Formula|
Lines and Angles:
Do you ever think that the house you live in has a straight walls inclined ladder and much more thing is so much confined to its shape?
The reason is simple that is by the use of lines and angles everything wears a perfect shape. You now must aware that how lines and angles are important to us.
Terminology related to lines and angles:
- Line: A collection of points which follows a straight path and can be drawn endlessly in both sides.
- Line Segment: A finite part of line is said to be line segment. It has two end-points.
- Ray: A line when cut at a point and its one end follows the infinite path is called ray. It has one end-point.
- Point of intersection: When two lines, we say they intersect; the meeting point is called the point of intersection.
- Angle: When two line or line segment intersects then at the intersecting point angles are formed.
Terms related to angles:
- Complementary Angles: When the sum of the measures of two angles is 90°, the angles are called complementary angles.
Whenever two angles are complementary, each angle is said to be the complement of the other angle.
These two angles are complementary.
- Supplementary Angles: When the sum of the measures of two angles is 180°, the angles are called complementary angles.
When two angles are supplementary, each angle is said to be the supplement of the other.
These two angles are supplementary.
- Adjacent Angles: The condition of angle to be adjacent angles are they must have a common vertex, a common arm, and the non-common arms are on either side of the common arm.
The angles 1 and two are adjacent angles.
- Linear Pair: A linear pair is a pair of adjacent angles whose non-common sides are opposite rays.
Also, say if sum of adjacent angle is 180⁰ then the angles are in linear pair.
Sum of angle 1 and 2 is 180⁰.
- Vertically Opposite Angles: When two lines intersect then the angles lying opposite the angle we took is called vertically opposite angles.
When two lines intersect, the vertically opposite angles so formed are equal.
Angle 1 & 3 and 2 & 4 are vertically opposite angles.
Terms related to lines:
Intersecting Lines: When two lines are drawn on paper either intersect or when extended intersects is called intersecting lines.
Parallel lines: When two lines drawn on a paper doesn’t meet if extended to infinity is said to be parallel lines.
Transversal line: A line that intersects two or more distinct points is called transversal.
Example: p is a transversal to the lines l and m.
Angles Made by Transversal:
|Interior Angles||∠3, ∠4, ∠5, ∠6|
|Exterior Angles||∠1, ∠2, ∠7, ∠8|
|Pairs of Corresponding Angles||∠1 and ∠5, ∠2 and ∠6, ∠3 and ∠7, ∠3 and ∠7, ∠4and ∠8,|
|Pairs of Alternate Interior Angles||∠3 and ∠6, ∠4 and ∠5,|
|Pairs of Alternate Exterior Angles||∠1 and ∠8, ∠2 and ∠7,|
|Pairs of Interior Angles on the same side of Transversal.||∠3 and ∠5, ∠4 and ∠6,|
Transversal of Parallel Lines:
- If two parallel lines are cut by a transversal then each pair of alternate interior angles are equal.
- If two parallel lines are cut by a transversal, then each pair of interior angles on the same side of the transversal are supplementary (i.e. sum of angle=180⁰).
- When a transversal cuts two lines, such that pairs of corresponding angles are equal, then the lines have to be parallel.