Download Geometry SOL Study Guide by the 14 standards

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