* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download Chapter 7
Survey
Document related concepts
Perspective (graphical) wikipedia , lookup
Lie sphere geometry wikipedia , lookup
Problem of Apollonius wikipedia , lookup
Duality (projective geometry) wikipedia , lookup
Technical drawing wikipedia , lookup
Multilateration wikipedia , lookup
Perceived visual angle wikipedia , lookup
Line (geometry) wikipedia , lookup
Rational trigonometry wikipedia , lookup
Pythagorean theorem wikipedia , lookup
Integer triangle wikipedia , lookup
Compass-and-straightedge construction wikipedia , lookup
History of trigonometry wikipedia , lookup
Trigonometric functions wikipedia , lookup
Transcript
CHAPTER 7 7-1 LINES AND PLANES • Point – a location, has no size, name point by capital letter • Line – series of points that extend in opposite directions without end • Ray – part of a line with one endpoint and all the points of the line on one side of the endpoint • Segment – part of a line with two endpoints and all points in between. 7-1 LINES AND PLANES • Plane – Flat surface that extends indefinitely in all directions and has no thickness • Intersecting Lines – have exactly one point in common • Parallel Lines – lines in the same plane that never intersect • Skew Lines – lie in different planes, they are neither parallel or intersecting 7-1 LINES AND PLANES 7-1 LINES AND PLANES Name segments that fit description. 1) parallel to BC 2) intersect BH 3) skew to AG 7-1 LINES AND PLANES-ANSWERS Name segments that fit description. 1) parallel to BC- HD 2) intersect BH – AB, BC 3) skew to AG – BC, HD 7-2 IDENTIFYING AND CLASSIFYING ANGLES Angle – figure formed by two rays with a common endpoint Vertex – point of intersection of two sides of an angle or figure 7-2 IDENTIFYING AND CLASSIFYING ANGLES Classify angles by their measures: 7-2 IDENTIFYING AND CLASSIFYING ANGLES Complementary angles – sum of the measures of two angles is 90° Supplementary angles – sum of the measures of two angles is 180° 1) Find complement of m<G = 79° 2) Find supplement of m<G = 12° 3) Find complement of m<G = 75.1° 4) Find supplement of m<G = 82.2° 7-2 IDENTIFYING AND CLASSIFYING ANGLESANS Complementary angles – sum of the measures of two angles is 90° Supplementary angles – sum of the measures of two angles is 180° 1) Find complement of m<G = 79° 11° 2) Find supplement of m<G = 12° 168° 3) Find complement of m<G = 75.1° 14.9° 4) Find supplement of m<G = 82.2° 97.8° 7-2 IDENTIFYING AND CLASSIFYING ANGLES Adjacent angles – share a vertex and a side. They are side by side. Vertical angles – formed by two intersecting lines and are opposite each other Congruent – same size and shape 7-2 IDENTIFYING AND CLASSIFYING ANGLES 7-2 IDENTIFYING AND CLASSIFYING ANGLESANS Right angle Obtuse angle Straight angle Acute angle Acute angle Right angle 7-2 IDENTIFYING AND CLASSIFYING ANGLES 1) Four right angles 2) Two pairs of obtuse vertical angles 1) two lines 2) Three segments 3) Pair of congruent angles 3) Two pairs of adjacent supplementary angles 7-2 IDENTIFYING AND CLASSIFYING ANGLESANS 1) two lines XU, ST, XP 2) Three segments XN, XP, QN 3) Pair of congruent angles <VXW and <UXP 1) Four right angLes <QNT, <SNQ, <SNY, <YNT 2) Two pairs of obtuse vertical angles <MSW AND <UST ; <SXP AND <VXW 3) Two pairs of adjacent supplementary angles <MSX AND <MSU; <MSX AND <XST 7-3 TRIANGLES Classifying Triangles by Sides: 7-3 TRIANGLES Classifying Triangles by angle measures: 7-3 TRIANGLES Classifying Triangles by angle measures: 7-3 TRIANGLES -ANS Classifying Triangles by angle measures: Obtuse scalene right isosceles acute isosceles 7-3 TRIANGLES Classifying Triangles by angle measures: 7-3 TRIANGLES-ANS Classifying Triangles by angle measures: isoseles right equilateral right obutse acute 7-3 TRIANGLES Angle Sum of a Triangle: - Sum of the measures of the angles of any triangle is 180° - All angles add up to 180° inside a triangle. 7-3 TRIANGLES-ANS Angle Sum of a Triangle: - Sum of the measures of the angles of any triangle is 180° - All angles add up to 180° inside a triangle. 40° 80° 64° 7-4 QUADRILATERALS AND OTHER POLYGONS Regular polygon – a polygon with all sides congruent and all angles congruent Irregular polygon – a polygon with sides that are not all congruent or angles that are not all congruent 7-4 QUADRILATERALS AND OTHER POLYGONS Trapezoid – one pair of parallel sides Parallelogram – both pairs of opposite sides parallel Rectangle – 4 right angles Rhombus – 4 congruent sides Square – 4 right angle angles and 4 congruent sides 7-4 QUADRILATERALS AND OTHER POLYGONS 7-4 QUADRILATERALS AND OTHER POLYGONSANS hexagon, regular pentagon, irregular Pentagon, regular parallelogram, irregular quadrilateral, irregular 7-5 CONGRUENT FIGURES Congruent Polygons – are polygons with the same size and same shape. Name corresponding parts. 7-5 CONGRUENT FIGURES-ANSWERS Congruent Polygons – are polygons with the same size and same shape. Name corresponding parts. 7-5 CONGRUENT FIGURES 7-5 CONGRUENT FIGURES-ANSWERS QR <R YW <X 7-5 CONGRUENT FIGURES 7-5 CONGRUENT FIGURES-ANSWERS Not congruent, because corresponding angles and sides are not congruent. Congruent, because corresponding angles and sides are congruent. 7-6 CIRCLES Circle – set of points in a plane that are all the same distance from a given point. Radius – segment that connects the center of a circle to circle. Chord – segment that has both endpoints on the circle. Diameter – chord that passes through the center of the circle; longest chord Central Angle – angle with a vertex at the center of the circle Arc – part of a circle Semicircle – is half a circle 7-6 CIRCLES Identify radius, chord, diameter, central angle, and arc. 7-6 CIRCLES 7-6 CIRCLES-ANSWERS FG, EF <FDG, <GDH FH Triangle FDG Arcs, FG, FGH, GH, HE, GHE 90° FH 7-7 CIRCLE GRAPHS Circle graph – graph of data in which a circle represents the whole. Total must be = to 100% Finding central angles: 7-7 CIRCLE GRAPHS 7-7 CIRCLE GRAPHS-ANSWERS 75 ° 60 ° 120 ° 48 20.8% 16.7% 33.3% 105 ° 29.2% 360° 100% 7-7 CIRCLE GRAPHS 7-7 CIRCLE GRAPHS-ANSWERS sleeping 12.5% About 8 hours