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Transcript
Math 4. Class work 27. Review of geometry. 1. There are four undefined terms in geometry: a point, a line, a plane, and a distance between two points. These terms are considered to be intuitively understood. 2. All other concepts and terms we can define based on these four, for example A line segment is a part of a straight line between two chosen points. (A set of points of a straight line between two points.) These points are called endpoints. A ray is a part of a straight line consisting of a point (endpoint) and all points of a straight line at one side of an endpoint. Ray is named by two ints endpoint and any other point, ray ሬሬሬሬሬԦ 𝐴𝐵 or AB ( where A is an endpoint) A circle is the set of all points in a plane that are at a given distance from a given point, the center. Parallel lines are lines in a plane which do not meet; that is, two lines in a plane that do not intersect or touch each other at any point are said to be parallel. Draw a circle and a straight line. 3. An angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle. Two angles are called adjacent if they have a common vertex and a common side. If two adjacent angles combined form a straight angle they are called supplementary, if they form a right angle than they are called complementary. When two straight lines intersect at a point, four angles are formed. A pair of angles opposite each other, formed by two intersecting straight lines that form an "X"-like shape, are called vertical angles or opposite angles or vertically opposite angles. and and and are 2 pairs of vertical angles. Vertical angle theorem: vertical angles are equal 4. Sum of the internal angles of a triangle is always equal to 180. 5. Sum of the internal angels of any polygon is (𝑛 − 2) × 180. 𝑛 × 180 − 360 = (𝑛 − 2) × 180 6. Construction with a compass and a straight edge. a. Draw a triangle with the sides are equal to the segments. b. Divide the segment by half.