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The three non-collinear points, are called the vertices of the triangle. The plane figure bounded by the union of three lines, which Join three non-collinear points. The ratio of intercepts made by three parallel lines on a transversal is equal to the corresponding intercepts made on any other transversal PR/RT=QS/SU Now, POS = ROQ = 105° (Vertically opposite angles)Īnd SOQ=POR = 75° (Vertically opposite angles) In figure given below, lines PQ and RS intersect each other at point O. The pairs of interior angles thus formed are supplementary. Interior angles: When two lines are intersected by a transverse, they form two pairs of interior angles. The pairs of alternate angles thus formed are congruent, i.e. When two lines are intersected by a transverse, they form two pairs of alternate angles. Vertically opposite angles are congruentĪlternate angles: In the above figure, 3 and 3, 2 and 8 are Alternative angles. Vertically Opposite angles: Two angles are called vertically opposite angles if their sides form two pairs of opposite rays. Supplementary angles: Two angles whose sum is 180° are supplementary, each one is the supplement of the other. The sum of the measures of the angles is 180°.Ĭomplementary angles: Two angles whose sum is 90°, are complementary, each one is the complement of the other. Linear Pair: Two angles are said to form a linear pair if they have common side and their other two sides are opposite rays.

An angle greater than 180° but less than 360° is called a reflex angleĪdjacent angles: Two angles are called adjacent angles if they have a Common side and their interiors are disjoint.

An angle greater than 90° but less than 180° is called an obtuse angle.

An angle less than 90° is called an acute angle.

The common origin is called the vertex and the two rays are the sides of the angle.Ĭongruent angles: Two angles are said to be congruent, denoted by if it divides the interior of the angle into two angles of equal measure.

Lines which are parallel to the same line are parallel to each other.Īngles: An angle is the union of two non-collinear rays with a common origin.

If two lines are perpendicular to the same line, they are parallel to each other.Every point on the perpendicular bisector of a segment is equidistant from the two endpoints of the segment.intersect at 900 and passes through the midpoint of die segment is called the perpendicular bisector of the segment A line which is perpendicular to a line segment, i.e.A line, which intersects two or more given coplanar lines in distinct points, is called a transversal of the given lines.

Two or more lines are said to be coplanar if they lie in the same plane, otherwise they are said to be non-coplanar.

Three or more points are said to be collinear if they lie on a line, otherwise they are said to be non-collinear.

Perpendicular lines: Two lines, which lie in a plane and intersect each other at right angles are called perpendicular lines. The distance between two parallel lines is constant. Parallel lines: Two lines, which lie in a plane and do not intersect, are called parallel lines. Line segment: A line with two end points is called a segment. Ray:A line with one end point is called a ray. It can be extended indefinitely in both directions.

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GEOMETRY PROBLEMS PDF

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