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Transcript

Geometry: Lines, line segments, rays, and angles 1 Notation and vocabulary for naming lines, line segments, and rays term diagram s s s ABC line s line segment A s A ray 2 notation ↔ notes ↔ AB or BA ok to use any pair of points but not all 3 s B AB or BA s B → - AB Angles • formally: union of 2 rays with a common endpoint, called vertex • more dynamic description of an angle: measurement of rotation naming angles: Name picture angle A A - 1 angle 1 Is D@ @ BAC C s @s A s B measuring angles 1 1 • unit: degree = 360 rotation; also minutes ( 60 of a degree) and seconds 1 1 ( 60 ) of a minute or 3600 of a degree) • tool: protractor • size of an angle is determined by its measure, not by how long the rays are drawn 1 3 Classifying angles Name Definition right angle an angle whose measure is 90◦ acute angle Picture 6 - * - an angle whose measure is between 0◦ and 90◦ I @ @ obtuse angle an angle whose measure is between 90◦ and 180◦ @ - AB(C straight angle an angle whose measure is 180◦ s A s B s C - reflex angle an angle whose measure is between 180◦ and 360◦ Note: It’s good to be familliar with the following angles. We can compare their size to that of a given angle in order to make reasonable estimates of the measure of the given angle. 30◦ 45◦ 2 60◦ 4 Relationships between angles Name Definition Picture Notes C s angles with the same vertex, a common side, and disjoint interiors adjacent angles * 2 1 s B A angles 1 and 2 are adjacent 2 6 1 - complementary angles two angles whose measures add to 90◦ angles 1 and 2 are complementary ABC is not adjacent to either angle 1 or angle 2 complementary angles do not need to be adjacent to each other 2 s 1 - supplementary angles two angles whose measures add to 180◦ angles 1 and 2 are supplementary 2 supplementary angles do not need to be adjacent to each other 1 4 vertical angles two non-adjacent angles formed when two lines intersect 3 angles 1 and 3 are vertical angles and angles 2 and 4 are vertical angles vertical angles are congruent (defined below) Important vocubulary and notation When two angles have the same measure, we say they are congruent (not equal). Notation: 6 ∼ 1=6 2 We can also say their measures are equal. Notation: 3 m6 1 = m6 2