lines n angles

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Lines and Angles

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Ray Line Intersecting Lines Parallel Lines Line Segment Types of Lines

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RAY : A part of a line, with one endpoint, that continues without end in one direction LINE : A straight path extending in both directions with no endpoints LINE SEGMENT : A part of a line that includes two points, called endpoints, and all the points between them

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INTERSECTING LINE : The two lines in the same plane are not parallel, they will intersect at a common point. Those lines are intersecting lines. Here C is the common point of AE and DB

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PARALLEL LINES : Lines that never cross and are always the same distance apart

Perpendicular Lines:

Perpendicular Lines Two lines that intersect to form a right angles

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Angles The figure formed when two rays share the same endpoint Right Angle: An angle that forms a square corner Acute Angle: An angle less than a right angle Obtuse Angle: An angle greater than a right angle

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Straight Angle : It is equal to 180° Reflex Angle : An angle which is more than 180° but less than 360°

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Complementary Angles : Two angles adding up to 90° are called complementary angles. Here  ABD + DBC are Complementary.

Supplementary Angles: Two angles adding up to 180° are called supplementary.:

Supplementary Angles : Two angles adding up to 180° are called supplementary. ABD +  DBC are supplementary

Transversal: A Transversal is a line that intersect two parallel lines at different points.:

Transversal : A Transversal is a line that intersect two parallel lines at different points.

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Vertical Angles : Two angles that are opposite angles 1 2 3 4 5 6 7 8 t 1   4 2   3 5   8 6   7

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Linear Pair : Two angles that form a line (sum=180  ) 1 2 3 4 5 6 7 8 t 5+  6=180 6+  8=180 8+  7=180 7+  5=180 1+  2=180 2+  4=180 4+  3=180 3+  1=180

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Corresponding Angles : Two angles that occupy corresponding positions are equal. 1   5 2   6 3   7 4   8 t 1 2 3 4 5 6 7 8

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Alternate Interior Angles : Two angles that lie between parallel lines on opposite side. 3   6 4   5 1 2 3 4 5 6 7 8

Co-Interior Angles: Two angles that lie between parallel lines on the same side of the transversal:

Co-Interior Angles : Two angles that lie between parallel lines on the same side of the transversal 1 2 3 4 5 6 7 8 3 + 5 = 180 4 + 6 = 180

Alternate Exterior Angles: Two angles that lie outside parallel lines on opposite sides of the transversal:

Alternate Exterior Angles : Two angles that lie outside parallel lines on opposite sides of the transversal 1 2 3 4 5 6 7 8 2   7 1   8

Angle Sum Property Of Triangle: The sum of the angles of a triangle is 180°.:

Angle Sum Property Of Triangle : The sum of the angles of a triangle is 180° . 1 2 3 1 + 2 + 3 = 180°

Property of Exterior Angle: If a side of a triangle is produced, then the exterior angle so formed is equal to the sum of the two interior opposite angles.:

Property of Exterior Angle : If a side of a triangle is produced, then the exterior angle so formed is equal to the sum of the two interior opposite angles. Angle 1,2,3 are exterior angles of triangle

Proof :

Vertically Opposite Angles are equal To Proof – Vertically Opposite Angles are equal Proof

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Solution - b + n = 180 ° ( LINEAR PAIR) b + m = 180 ° ( LINEAR PAIR) EQUATING BOTH THE EQUATIONS → b + n = b + m → n = m Hence Proved

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Angle Sum Property Of A Triangle is 180 ° To Proof - Angle Sum Property Of a Triangle is 180° Construction - Draw ↔m parallel to BC Solution - 4 =  1 (Alternate Interior Angles) 5 = 2 (Alternate Interior Angles)

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3 + 4 + 5 = 180 ° ( Angles on the same line are supplementary) Substituting the values 3 + 1 + 2 = 180 ° (Angle Sum Property) Hence Proved

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The End Made by: Rohan Dalmia

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