Lines and Angles. Fundamental concepts of Geometry:. Point: It is an exact location. It is a fine dot which has neither length nor breadth nor thickness but has position i. It has and points and a definite length. Ray: A line segment which can be extended in only one direction is called a ray.

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Embed Size px x x x x Fundamental concepts of Geometry: Point: It is an exact location. It is a fine dot which has neither length nor breadth nor thickness but has position i.

It has and points and a definite length. Ray: A line segment which can be extended in only one direction is called a ray. Intersecting lines: Two lines having a common point are called intersecting lines. The common point is known as the point of intersection. Concurrent lines: If two or more lines intersect at the same point, then they are known as concurrent lines.

Angles: When two straight lines meet at a point they form an angle. In the figure above, the angle is represented as AOB. Point O is the vertex of AOB. Right angle: An angle whose measure is 90o is called a right angle. Acute angle: An angle whose measure is less then one right angle i.

Obtuse angle: An angle whose measure is more than one right angle and less than two right angles i. Reflex angle: An angle whose measure is more than o and less than o is called a reflex angle.

Complementary angles: If the sum of the two angles is one right angle i. Therefore, the complement of an angle is equal to Supplementary angles: Two angles are said to be supplementary, if the sum of their measures is o. Example: Angles measuring o and 50o are supplementary angles.

Two supplementary angles are the supplement of each other. Therefore, the supplement of an angle is equal to Vertically opposite angles: When two straight lines intersect each other at a point, the pairs of opposite angles so formed are called vertically opposite angles. In the above figure, 1 and 3 and angles 2 and 4 are vertically opposite angles. Note: Vertically opposite angles are always equal.

Bisector of an angle: If a ray or a straight line passing through the vertex of that angle, divides the angle into two angles of equal measurement, then that line is known as the Bisector of that angle. Parallel lines: Two lines are parallel if they are coplanar and they do not intersect each other even if they are extended on either side. Transversal: A transversal is a line that intersects or cuts two or more coplanar lines at distinct points.

In the above figure, a transversal t is intersecting two parallel lines, l and m, at A and B, respectively. Angles formed by a transversal of two parallel lines:. In the above figure, l and m are two parallel lines intersected by a transversal PS. Therefore, lines P, R, S and U are parallel to each other. Similarly, lines Q and T are parallel to each other.

Let the line PQ and RS be parallel. In the figure given below, lines AB and DE are parallel. What is the value of CDE? General Properties of Triangles: 1. The two sides of a triangle are 12 cm and 7 cm. If the third side is an integer, find the sum of all the values of the third side.

Answer: Let the third side be of x cm. Therefore, minimum value of x is 6. Therefore, the highest value of x is The sum of all the integer values from 6 to 18 is equal to Also, the exterior angle is equal to sum the two opposite interior angle A and B, i. The medians of a triangle are lines joining a vertex to the midpoint of the opposite side.

The point where the three medians intersect is known as the centroid. O is the centroid in the figure. The medians divide the triangle into two equal areas. Answer: The figure is shown below. O bisects AC and BD. The altitudes are the perpendiculars dropped from a vertex to the opposite side. Triangle ACE is a right-angled triangle. Therefore, AHC and B are supplementary angles.

Internal Angle Bisectors of a Triangle:. The point of intersection of these angle bisectors, I, is known as the incentre of the triangle ABC, i. In figure above, O is the centre of the circle and BC is a chord. Therefore, the angle subtended at the centre by BC will be twice the angle subtended anywhere else in the same segment. It can be proved that:. Home Documents Geometry by Total Gadha. Post on Oct 1. Category: Documents download. A point on an angle is equidistant from both the arms.

Angles formed by a transversal of two parallel lines: In the above figure, l and m are two parallel lines intersected by a transversal PS. Medians of a triangle: The medians of a triangle are lines joining a vertex to the midpoint of the opposite side. Find the length of AC. Altitudes of a Triangle: The altitudes are the perpendiculars dropped from a vertex to the opposite side.

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## geometry by total gadha

Embed Size px x x x x Fundamental concepts of Geometry: Point: It is an exact location. It is a fine dot which has neither length nor breadth nor thickness but has position i. It has and points and a definite length. Ray: A line segment which can be extended in only one direction is called a ray. Intersecting lines: Two lines having a common point are called intersecting lines.

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