Lines and Angles

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Three or more points that lie on the same line are called collinear points. If points do not lie on the same line, they are called non-collinear points.

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Two angles are adjacent if they have: (1) A common vertex, (2) A common arm, and (3) Their non-common arms are on different sides of the common arm. When two angles are adjacent, their sum equals the

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Complementary angles: Two angles whose sum is 90°. Supplementary angles: Two angles whose sum is 180°. Example: If one angle is 30°, its complement is 60° and its supplement is 150°.

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If a ray stands on a line, then the sum of two adjacent angles so formed is 180°. This means when a ray divides a straight line into two angles, those angles are supplementary.

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If the sum of two adjacent angles is 180°, then the non-common arms of the angles form a line. This is the reverse statement of Axiom 6.1.

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When two lines intersect, they form two pairs of vertically opposite angles. Vertically opposite angles are always equal. For example, if two lines intersect at point O, then ∠AOC = ∠BOD and ∠AOD = ∠B

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Theorem 6.1: If two lines intersect each other, then the vertically opposite angles are equal. This can be proved using the Linear Pair Axiom.

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A transversal is a line that intersects two or more other lines at distinct points. When a transversal cuts two parallel lines, it creates eight angles with special relationships.