* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download Geometry SOL Study Guide by the 14 standards
Survey
Document related concepts
Problem of Apollonius wikipedia , lookup
Lie sphere geometry wikipedia , lookup
Perspective (graphical) wikipedia , lookup
Riemannian connection on a surface wikipedia , lookup
Technical drawing wikipedia , lookup
History of geometry wikipedia , lookup
Perceived visual angle wikipedia , lookup
Line (geometry) wikipedia , lookup
Multilateration wikipedia , lookup
Rational trigonometry wikipedia , lookup
Integer triangle wikipedia , lookup
Compass-and-straightedge construction wikipedia , lookup
Trigonometric functions wikipedia , lookup
Pythagorean theorem wikipedia , lookup
History of trigonometry wikipedia , lookup
Transcript
Geometry SOL Study Guide by the 14 standards of SOL’s G.1 Conditional statements: If p, then q. p > q Hypothesis and conclusion Converse: If q, then p. q>p Inverse: If not p, then not q. ~p > ~q Contrapositive: If not q, then not p. ~q > ~ p Venn DiagramsG.2 Transformations: Translations, slide Reflection use ( x, y ) ordered pairs Rotations Symmetric with a line or a point #2 given two points ( x, y) find the distance, midpoint, slope write down formulas Distance d x1 x2 y1 y2 Midpoint M ( 2 x1 x2 y1 y2 , ) 2 2 2 or use the Pythagorean Theorem rise and run Slope = y y rise or 1 2 run x1 x2 G.3 Pairs of angles and parallel lines A. complementary (90), supplementary (180), linear pair(180), vertical angles (=), B. Parallel line and transversal: alternate interior and exterior(=), corresponding (=), same-side interior ( 180) C. Angles of a polygon; sum of interior s= (n-2)180 sum of exterior = 360 One interior + one exterior = 180 G.4 parallel lines and transversal determine if 2 lines are parallel use above angles in G.3 G. 5 Triangles; Congruent: SSS, SAS,ASA, AAS Similar triangles: proportions ( cross-multiply), scale factor 1 to2 size same shape, different G. 6 Triangle inequality; list sides or angles in order according to largest angle or side Longest side is across from largest angle or vice-versa #2 Sum of any two sides is greater than 3rd side sum of two smallest is more than 3rd. #3 given two sides find range of third side by subtracting and adding two sides Ex. Given 15 and 26 as two sides then the 3rd side is between 11> 41 G.7 right triangles Pythagorean theorem a 2 b 2 c 2 know your triples: 3,4,5 5,12,13 7, 24,25 8,15,17 9, 40, 41 Sin, Cos, Tan SOH-CAH-TOA use table or calculator Radicals and Square roots G.8 Quadrilaterals: Parallelograms; rectangle, square, rhombus Trapezoid : Isosceles trapezoid and median of trapezoid Know properties of each and diagonals pg 330-332 in book G.9 Polygons: know the names of each, regular polygon: sides, angles congruent Sum of interior angles Sum= (n-2)180 sum of exterior angles = 360 One interior + one exterior = 180 forms a linear pair Tessellations and in order to not have any gaps, angles need to go into 360 G.10 Circles: know terms of circles: center, radius, diameter, chord, secant, tangent, arcs, arc length and arcs and angles measurements: central angle, inscribed angle, Angle inside circle, angle outside circle, segments with chords, secant, or tangent Book page 506-508 G.11 Constructions use tools on menu bar or a corner of piece of paper: Congruent segments or angles, bisector of angle or segment, perpendiculars G.12 3-dimensional shapes: view points, models G.13 Surface area and volume of solids: prisms, cylinders, cones, pyramids, sphere Will have a formula sheet with all formulas on it G.14 proportions of similar solids Change in one dimension of an object affects area or volume: Ratios are the following: a : b a 2 : b2 for area a3 : b3 for volume Example double(x 2) the height it will be four times for area ( 22 ) And 8 times for volume ( 23 ) = 8 times larger