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Geometry finals
studing for the geometry finals
| Question | Answer |
|---|---|
| reflections x-axis | (x,y)->(x,-y) [1,0 0,-1] |
| reflections y-axis | (x,y)->(-x,y) [-1,0 0,1] |
| reflections y=x | (x,y)->(y,x) [0,1 1,0] |
| reflections y=-x | (x,y)->(-y,-x) [0,-1 -1,0] |
| Rotations (about origin) 90 CW | (x,y)->(y,-x) [0,1 -1,0] |
| Rotations (about origin) 270 CC | (x,y)->(y,-x) [0,-1 -1,0] |
| Rotations (about origin) 180 CW or CC (same) | (x,y)->(-x,-y) [-1,0 0,-1] |
| Rotations (about the origin) 270 CW | (x,y)->(-y,x)[0,-1 1,0] |
| Rotations (about the origin) 90 CC | (x,y)->(-y,x) [0,-1 1,0] |
| sum of interior angles of a regular polygon | (n-2)180 |
| Each interior angle of a reg polygon | (n-2)/n(180) |
| sum of the exterior angles | 360 |
| each exterior angles of a regular polygon | 360/n |
| Pythagorean Theorem | a^2+b^2=c^2 |
| Pythagorean Theorem:acute | a^2+b^2>c^2 |
| Pythagorean Theorem:obtuse | a^2+b^2 |
| Area of a square | s^2 |
| Area of a rectangle | lw |
| Area of a triangle | (1/2)bh |
| Area of a Rhombus | (1/2)(d1+d2) |
| Area of a Trapezoid | (1/2)h(b1+b2) |
| area of a regular polygon | (1/2)ap |
| Area of a Circle | (pi)r^2 |
| circumference of a circle | (pi)d |
| Arc Length of a circle | 2(pi)r(x/360) |
| Area of a sector in a circle | (x/360)(pi)r^2 |
| Standard Form of the Equations of a circle | (x-h)^2+(y-k)^2=r^2 |
| Surface (total) area of a Sphere | 4(pi)r^2 |
| Volume of a Sphere | (4/3)(pi)r^3 |
| Sine | SOH |
| cosine | CAH |
| Tangent | TOA |
| Converse | If Q, then P |
| Inverse | If not P,then not Q |
| Contrapositive | If not Q,then not P |
| Biconditional | P,if and only if,Q |
| Statement | If P,then Q |
| Signs:Inverse | ~P-~Q |
| Signs:Converse | Q-P |
| signs:Biconditional | P<->Q |
| signs:Contrapositive | ~Q-~P |
| Alternate angles are | congruent |
| Consecutive angles are | supplementary |
| corresponding angles are | congruent |
| exterior angles are | congruent |
| sum of complementary angles are | 90 degrees |
| sum of supplementary angles are | 180 degrees |
| ways triangles are congruent | SSS,SAS,ASA,AAS,HL |
| ways triangles are similiar | SSS,ASA,AA |
| Measure of a central angle | measure of intercepted arc |
| measure of inscribed angled | (1/2)measure of intercepted arc |
| measure of angled formed by 2 chords inside a circle | (1/2)sum of intercepted arcs |
| measure of angles formed secants and/or tangents outside a circle | (1/2)difference of intercepted arc |
| ratio of the perimeters | x:4 |
| ratio of the areas | x^2:y^2 |
| ratio of the volumes | x^3:y^3 |
| distance formula | (sq.rtof:(x2-x1)^2+(y2-y1)^2) |
| slopes of parallel lines | same |
| slopes of perpendicular lines | recipricals |
| slope intercept form | y=mx+b |
| point slope form | y-y1=m(x-x1) |
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