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 Diagrams-

G.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 [pic] or use the Pythagorean Theorem rise and run

Midpoint [pic] Slope = [pic]

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 same shape, different size

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 [pic] 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: [pic]

Example double(x 2) the height it will be four times for area ([pic])

And 8 times for volume ([pic] = 8 times larger

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