Transcript Chapter 2
Chapter 2 Introducing Geometry Lesson 2.1 • Definition – a statement that clarifies or explains the meaning of a word or a phrase. • Point – an undefined term. The basic unit of geometry. It has no size, is infinitely small, and has only location. Named with a capital letter. • Line – an undefined term. A straight arrangement of points. There are infinitely many points in a line. A line has infinite length but no thickness and extends forever in two directions. Named with two capital letters representing points and a line over. M N • Plane – an undefined term. A plane has length and width but no thickness. It is a flat surface that extends forever. • Collinear points – two or more points that lie on the same line or segment. D C E Coplanar points – two or more points that lie on the same plane. F H G • Space – the set of all points. Line segment – two points and all the points between them that lie on the line containing the two points. The two points are called the endpoints of the line segment. I J • Ray – ray AB is the part of the line AB that contains point A and all the points on line AB that are the same side of point A as point B. A is the endpoint. A B • Angle – two rays that share a common endpoint provided the two rays do not lie on the same line. R S T Vertex – the corner of the angle. In this picture it is S. Lesson 2.2 • Congruent – two geometric figures are congruent if and only if they are identical in shape and size. U X V W Y B1 Z A1 Lesson 2.3 • Conditional statement – a statement that can be expressed as an if-then statement. For example “If a polygon is a hexagon, then it has exactly six sides.” • Converse – the statement formed by reversing the two parts of a conditional statement. For example “If a polygon has exactly six sides, then it is a hexagon.” Biconditional statement – a statement in which a conditional statement and its converse are both true and are combined into one statement. “A polygon is hexagon if and only if it has exactly six sides.” Counterexample – an example that proves a statement wrong. • Right angle – an angle whose measure is 90 degrees. B C A • Acute angle – an angle whose measure is less than 90 degrees. B A C D E F • Obtuse angle – an angle whose measure is greater than 90 degrees. A C B D E F • Midpoint of a segment – the middle of the segment such that it divides the original segment in half. A C B • Angle bisector – a ray that has an endpoint on the vertex of an angle and that divides the angle into two angles of equal measure. A B C Lesson 2.4 • Parallel lines – two or more lines that lie in the same plane and that do not intersect. • Skew lines – lines that are not in the same plane and do not intersect. • An example of this would be a pencil through a piece of paper. • Perpendicular lines – two lines that intersect to form a right angle. • Complementary angles – two angles whose measure have the sum of 90 degrees. mABC = 30.20 mDEF = 59.75 C A E D B F • Supplementary angles – two angles whose measure have the sum of 180 degrees. mHIG = 126.38 mJKL = 53.79 G H I K J L • Vertical angles – two lines intersect and the angles that are across from each other. N M Q O P • Linear pair of angles – two angles that form a line. T R S U Lesson 2.5 • Polygon – a closed geometric figure in a plane in which line segments connect endpoint to endpoint and each segment intersect exactly two others. • Convex polygons • Concave polygons Classify polygons Sides Name Sides Name Sides Names 3 Triangles 7 Heptagon 11 undecagon 4 Quadrilateral 8 Octagon 12 Dodecagon 5 Pentagon 9 Nonagon 6 Hexagon 10 Decagon N n-gon • Consecutive – they are right next to each other. • Perimeter – the sum of the lengths of all the sides. • Diagonal of a polygon – a segment connecting any two nonconsecutive vertices. • Equilateral polygon – a polygon whose sides are equal in measure. • Equiangular polygon – a polygon whose angles are equal in measure. • Regular polygon – a polygon that is both equilateral and equiangular. Lesson 2.6 • Right Triangle – a triangle with exactly one right angle. • Acute triangle – a triangle with three acute angles. • Obtuse triangle – a triangle with exactly one obtuse angle • Scalene triangle – a triangle with three sides of different lengths. • Isosceles triangle – a triangle with at least two sides the same length. • Equilateral triangle – a triangle with all sides equal. • Median of a triangle – a segment connecting the midpoint of a side to the opposite vertex. V Z X A1 Y W • Altitude of a triangle – a perpendicular segment from a vertex to the opposite side of the line containing the opposite side. V X B1 W Lesson 2.7 • Trapezoid – a quadrilateral with exactly one pair of parallel sides. A D B C • Kite – a quadrilateral with exactly two pairs of distinct congruent consecutive sides. • Parallelogram – a quadrilateral in which both pairs of opposite sides are parallel. • Rhombus – an equilateral parallelogram. • Rectangle – an equiangular parallelogram • Square – an equiangular rhombus and equilateral rectangle. Lesson 2.9 • Locus of points – the set of all points in a plane that satisfy some given condition or property.