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Angles
An angle is formed when lines or line segments meet.
The lines that form an angle are called the sides or the arms of the angle.
The common end point is called the vertex of the angle.
The angle formed by two lines or line segments can be an acute angle, where the measure of the angle is less than 90°.
The angle formed by two lines or line segments can be a right angle, where the measure of the angle is90°.
The angle formed by two lines or line segments can be an obtuse angle, where the measure of the angle is greater than 90°.
The angle formed by two lines or line segments can be a straight angle, where the measure of the angle is equal to 180°.
The angle formed by two lines or line segments can be a reflex angle, where the measure of the angle is greater than 180°.
When the sum of the measures of two angles is 90°, the angles are called complementary angles.
When the sum of the measures of two angles is 180°, the angles are called supplementary angles.
Adjacent angles have a common vertex and a common arm, and the noncommon arms are on either side of the common arm.
A linear pair is pair of adjacent angles whose noncommon sides are opposite rays.
Vertically opposite angles are opposite to each other and are equal.
Adjacent angles have no common interior points.
The angles in a linear pair are supplementary.
Angles may have a common vertex and a common arm.
Two angles are said to be adjacent angles if they have a common side or arm.
Two adjacent angles can be either supplementary or complementary.
If two adjacent angles are supplementary, then they form a straight angle, and are also called a linear pair.
Two angles that are not adjacent but have a common vertex are called vertically opposite angles.
Vertically opposite angles are equal
Pairs of Lines
Lines that meet at a point are called intersecting lines.
Lines that meet at a point are called intersecting lines.
Lines that always remain the same distance apart and never meet are called parallel lines.
A line that intersects two or more lines at distinct points is called a transversal.
When two lines are intersected by a transversal, pairs of corresponding angles, alternate angles and interior angles are formed.
Angles formed on the same side of a transversal, on the same side of the two lines and at corresponding vertices are called corresponding angles.
Angles formed on the opposite sides of the transversal at the two distinct points of intersection and between the two lines are called alternate interior angles.
Angles formed on the opposite sides of the transversal at the two distinct points of intersection but outside the two lines are called alternate exterior angles.
Angles that have different vertices, lie on the same side of the transversal and are interior angles are called consecutive interior angles or allied or cointerior angles.
Each pair of interior angles on the same side of the transversal are supplementary, each pair of corresponding angles are equal and each pair of alternate interior angles are equal. If a transversal cuts two lines such that the pairs of corresponding angles are equal, then the lines are parallel.
Eight angles are formed when a transversal intersects two lines.
The angles that lie between the lines are called interior angles.
The angles that lie on the outer sides of the lines are called exterior angles.
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