LINES AND ANGLES

• By admin
• March 14, 2023
• Dial Jio, Dial Me, Education, Teaching, Technology, Tips

Geomotrey : Geometry is the branch of mathematics in which we study solids, solid surfaces areas, lines, angles, points etc.

Solids : A solid is defined as the body which occupies space and has the boundary.

Line : A geometrical figure which has length and no breadth. It is called a line.

Point : It does not have length, breadth or thickness.

Space : It has the concept of emptiness and defined as the set of all points in our world.

Postulate : Postulate is the assumption of some relation of a starting point.

Theorem : Theorem is the result derived on the basis of postulates and common

logic.

Angle : It is defined as the union of two rays having the same end point. Angles are of several types given below :

• Zero Angle : Zero angle is defined as the angle in which the initial and final

position of a ray coincide without any rotation.

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• Right Angle : This is the angle

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in which the final position of a ray is one fourth of the complete rotation i.e. 360⁰

—— = 900. The angle between the initial and final position is equal to the 900. 4

• Straight Angle : If OA and OB are the initial and final positions of ray such that OA and OB are opposite rays, then the angle made between the opposite rays is known as straight It is an angle of 180⁰.

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• Acute Angle : The angle more than 0⁰ and less then 90⁰ is called acute

angle.

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• Obtuse Angle : The angle which is more than 90⁰ but less than 180⁰ is called an obtuse

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• Reflex Angle : The angle which is more than 1800 but less than 3600 is called a reflex

Particular types of angles :

• Supplementary Angles : Supplementary angles are the two angles, whose

sum is 1800. <A + <B = 1800.

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• Complementary Angles : These are two angles, whose sum is 90⁰.

<1 + <2 = 90⁰

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• Adjacent Angles : Two angles are said to be adjacent angles having common vertex and common arm and two other arms lie on opposite side of the common

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• Congruent or equal Angles : Two angles are said to be equal if they have the same
• Linear pair : Two adjacent angles form a linear pair if their non-common arms are two opposite
• Vertically opposite angles : Any two angles, which are formed by

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tow intersecting lines are called vertically opposite angles which are always equal.

• Angle at a point : Its rays OA, OB, OC, OD and OE having a initial point O, from <1, <2, <3, <4 and <5 at O then <1 + <2 + <3 + <4 + <5 = 3600.

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Transversal : A line that intersects two or more lines at different points is known as a transversal. AB is a transversal.

1. Interior Angles : The angles shown as 3,4,5,6 are known as interior

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2. Exterior Angles : The angles shown as 1, 2, 7, 8 are known as exterior
3. Corresponding Angles : In the figure, the angles : (1,5); (4,8); (2,6); (3,7) are called corresponding
4. Alternate Angles : In the figure, the angles (3,5); (4,6) are known as alternate

Parallel lines : Two lines are said to be parallel to each other, if

• they do not meet any where
• they are coplanar.

They have the following characteristics :

• The separation between two parallel lines is equal at all
• Through a point away from the given line, one and only one line parallel to the given line can be

THEOREMS

1. If a transversal intersects two parallel lines, then cuts pair of each correspond- ing angles are On the other hand, if a transversal intersects two lines, in which pair of corresponding angles are equal, then the lines are parallel.
2. If a transversal intersects two parallel lines, then the alternate interior angles

are equal.

3. If a transversal intersects two parallel lines, then consecutive interior angles are
4. In case a transversal intersects two lines in such a way that a pair of alternate interior angles are equal, the two lines are
5. If a transversal intersects two lines such that a pair of consecutive interior angles are supplementary, then the two lines are
6. Lines parallel to the same lines are parallel to one another
7. If a line is perpendicular to one of the two given parallel lines, it is also perpendicular to the other

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