MTH 152 Lecture Notes - Lecture 10: Solar Energy Generating Systems, Deductive Reasoning, Acute And Obtuse Triangles
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● Mathematical Systems: consists of undefined terms, definitions, axioms, and theorems
○ must always be some words that are undefined (ex: “Line”)
○ undefined terms: To avoid this problem of circularity, certain basic
words (ex: point, line, plane)
■ words are then used in definitions to define other words
○ Axioms: statements that we assume to be true and do not try to prove
○ Theorems: reason we use axioms, definitions, and undefined terms are used
together with deductive reasoning to prove theorems
● Line: set of points that we describe intuitively as being “straight” and extending
indefinitely in both direction
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○ Collinear: when 2 or more points are on the same line
● Plane: “flat” like the top of a table, but extending indefinitely
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○ Half-planes: formed when line in a plane partitions the plane into 3 separate sets:
the points on the line and 2 half-planes
■
● line segment: 2 points on a line and all the points between them
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○ Bisection: divide line seg. into 2 parts of equal length
○ Midpoint: point between endpoints
● Half-line: point on line separates line into 3 separate sets: the point and two half-lines
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● Ray: line with a single endpoint (or point of origin) that extends infinitely in one direction.
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● Angle: formed by the union of two rays, with a common endpoint
○ Vertex: endpoint of angle
○ sides of the angle: rays/line segments
● Angle measurements
○ Degrees: method for measuring angles by dividing a circle into 360 equal parts
○ One degree (1°) is 1/360 of a complete turn in a circle
○ Minutes: Each degree can be divided into 60 equal parts
○ Seconds: each minute can be divided into 60 equal parts
● Types of angles
○ right angle: If an angle has a measure of 90°
○ Acute angle: less than 90°
○ obtuse angle: more than 90° and less than 180°
○ straight angle: 180°
○ reflex angle: more than 180° and less than 360°
■ draw a circular arc to connect the two sides of this angle
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○ Complementary angles: sum of two angles is 90°
○ Supplementary angles: sum is 180°
○ adjacent angles: If two angles have the same vertex, share a common side, and
do not overlap
■
○ Vertical angles (across from eachother): Nonadjacent angles formed by two
intersecting lines; have equal measure