GEOMETRY 1 Basic definitions of some important term:

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Cecily Lawson
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2 GEOMETRY 1 Geometry: The branch of mathematics concerned with the properties and relations of points, lines, surfaces, solids, and higher dimensional analogues. GEOMETRY WHT TO STUDY? LSSIFITION OF NGLES LSSIFITION OF TRINGLES TRINGLES & THEIR PROPERTIES IRLES & THEIR PROPERTIES asic definitions of some important term: Point: Line: Straight Line: Line Segment: Ray: oncurrent Line: Intersection Line: dimension less figure used to define any location in a artesian system is known as the point. Two or more Points connected by a locus is known as a line. Shortest distance between two points covered by a locus is known as straight line. straight line fixed by two points at both its ends is known as line segments. straight line fixed at one end only is known as ray. Number of lines passing from a same point are known as concurrent line. Intersecting lines are two lines that share exactly one point. This shared point is called the point of intersection.

3 Parallel Line: Transversal Line: ngle: Perpendicular: ngle isector: Median: Parallel lines are two lines that are always the same distance apart and never touch. In order for two lines to be parallel, they must be drawn in the same plane, a perfectly flat surface like a wall or sheet of paper. In geometry, a transversal is a line that passes through two lines in the same plane at two distinct points. The space (usually measured in degrees) between two intersecting lines or surfaces at or close to the point where they meet. t an angle of 90 to a given line, plane, or surface or to the ground. n angle bisector is a line or ray that divides an angle into two congruent angles. Lines passing from the midpoint of a line is known median for that line. Perpendicular isector: The perpendicular bisector is a line that divides a line segment into two equal parts. It also makes a right angle with the line segment. cute ngle: Straight ngle: Right ngle: Reflex ngle: Obtuse ngle: n angle that measures less than ninety degrees, but more than zero degrees. t angle of 180. t angle of 90. The reflex angle is the larger angle. It is more than 180 but less than 360 n obtuse angle is a form of angle that measures more than 90 and less than 180.

IMPORTNT QUESTIONS Vertical opposite ngle 1= 4 ; 1= 4 2 = 3 ; 5 = 8 orresponding ngle 1= 5 ; 2= 6 3 = 7 ; 4 = 8 7 lternate ngle 3 = 6; 4 = 5 (Interior alternate angle) 1 = 8; 2 = 7 (Exterior

4 IMPORTNT QUESTIONS Vertical opposite ngle 1= 4 ; 1= 4 2 = 3 ; 5 = 8 orresponding ngle 1= 5 ; 2= 6 3 = 7 ; 4 = 8 7 lternate ngle 3 = 6; 4 = 5 (Interior alternate angle) 1 = 8; 2 = 7 (Exterior alternate angle) The sum of the angles formed by joining angle bisector of interior angles of parallel is 180 o. LINER PIR OF NGLES O and O are adjacent angles and O is a straight line. Such angles is called linear pair angles

5 LSSIFITION OF TRINGLES If c is the longest side then- a 2 +b 2 > c 2 (cute angled Triangle) a 2 +b 2 = c 2 (Right angled Triangle) a 2 +b 2 < c 2 (Obtuse ngled Triangle) The sum of angles of a triangle is The exterior angle is equal to the sum of the two interior opposite angles. The two sides are equal, then corresponding angles are equal. Sine Rule: Sin Sin = a b = Sin OSINE RULE: c os = b2 +c 2 a 2 2bc os = a2 +c 2 b 2 2ac os = a2 +b 2 c 2 2ab c a b

6 PYTHGORS THEOREM In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides 2 = GEOMETRY LINE NGLES In Triangles, the sides and are produced to points E and D respectively. O and O are the bisectors of E and D respectively meet at point O, then O In Triangles, O and O is the internal bisectors of and respectively meet at point O, then O O E O D

7 EX Sol: Ex: If three lines X,Y,Z are parallel lines then find F in the given figure : Ex: In the given figure. If PQ RS, QPT = and PTR = 20 0, then SRT is equal to: Sol. Here QPL + PLS =180 0 Ex: Sol. PLS = QPL Q =65 0 SLP = LRT + RTL LRT = RLP = = 45 0 SRT = = LTR In the given figure PQ RS, then find the value α + β + γ? PQ OM MOQ = β α RS OM X Y Z 125 o 80 o MOS = α β MOS = VOT = β α P Q P R M S R D L S E 30 o O γ F T V T

8 = β α α + β + γ = Ex: Sol: In, =, = 40 0.Then the external angle at is In, =, So = = = = = D = D = D 40 0

9 NOTES

Line: It s a straight arrangement of points that extends indefinitely in opposite directions.

More Terminology and Notation: Plane: It s an infinitely large flat surface. Line: It s a straight arrangement of points that extends indefinitely in opposite directions. ollinear Points: Points that lie