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Gre Math Alg, Geom

part I. Formulas & methods for Triangles, Proportions, Geometry,

QuestionAnswer
How do you solve two simultaneous equations? find x 2x+ 5y= 20; 6x-1/2y=29 alter to create problem that will result in isolation of desired variable. then compute; (10)6x-1/2y=29 60x-5y=290 2x + 5y = 20 62x=310
the measure of degrees along a straight line is how many degrees? a straight line measures 180deg.
the sum of all angles formed when 2 lines intersect = how many degrees? >The sum of all angles when two lines intersect = 360. >opposite angles are equal to eachother
what angle is formed by two perpendicular lines? two perpendicular lines form a right angle
what kind of triangle has three angles of 60 degrees? an equal lateral triangle has three angles of 60 degrees.
how do you make a right angle out of an equal lateral triangle? draw line through the middle
What kind of triangle is characterized by having two equal sides, and thus two equal angles? an Isosceles triangle has two equal sides and the angles of those two sides are equal.
> A of triangle = >>how does this relate to calculating the area of a quadrilateral? > A of Triangle = 1/2 x BH >> this realates to the A of a square by the fact that we only measure 1/2 the base, if we took BH we would get the A of a quadrilateral, which is 2x any given triangle
a 3-4-5 Triangle is characterized by what? 3-4-5 Triangle is proportional to a given common multiple. thus: short side = 3, long side = 4, Hypoteneuse = 5 the actual length in any unit is not the key, only the proportion of the sides in relation to eachother.
if a triangle has the following measurements: s1=15, s2=20, s3=25 what type of triangle is it? a triangle with the measurements of 15, 20, 25 is a 3-4-5 Triangle. (3x5)=15,(4x5)=20,(5x5)=25
a 5-12-13 Triangle is characterized by what? a ratio of (5x)(12x)(13x)
If you have a trangle w/ s1=10, s2= 24, Hypoteneuse=? What kind of trangle is this? A Triangle has s1=10, s2=24; the Hypoteneuse= 26 is a 5-12-13 Triangle
x: x^sq rt (3): 2x = what kind of Triangle proportions? x : x^sq rt (3) : 2x = 30:60:90 degree triangle
if we have a triangle who's side lengths are in the ratio of; 1: 1: (square root of 2)... a) What kind of Triangle do we have? b) What are the internal angles? In a triangle where the ratio of the sides are; 1:1: (sq rt 2);... a) This is an Isosceles triangle b) the angles are 45-45-90
What are the measurements of the internal angles of an Isosceles Triangle? The internal angles of an Isosceles Triangle are 45-45-90 degrees
A triangle who's side lengths are s1=5, Hypoteneuse=10,... a) What is the L of s2? b,c) What kind of Triangle do we have? What kind of Triangle is it? b) What are the internal angles? Where there is a triangle w/ s1=5, Hypoteneuse=10 a) s2= 5^sq rt (3) b,c) The degree measurements of s1=30, s2= 60, Hypoteneuse=90 Thus, it is a 30-60-90 degree Triangle
Pythagoeran Theorem: > Formula, Application, Limitations Pythagoeran Theorem: a^2+b^2=c^2 >When you have 2 sides of a RIGHT Triangle, use to find Hypoteneuse
If you divide a Right Triangle in a way which creates two smaller Right Triangles, >What is the characteristic of the resulting two Triangles in relation to the origional? If you divide a Right Triangle in a way which creates two smaller right triangles,: >the resulting sides of the small triangles are proportional to the sides of the origional
Circumference of a Circle =.... Circumference of a Circle = 2 (phi) (r)
Area of Circle =..... Area of Circle = (Phi) 2r
# of degrees in an angle formed by two radii at the center of a circle= ? (in relation to arc formed by their rotation) the # of degrees in an angle formed by two radii at the center of a circle= the measure of degrees of the Arc formed by the two radii.
What is a Trapezoid characterized by? How do you calculate its' Area? A Trapezoid is: > a quadrilateral w/ four sides of different length > Area of Trapezoid = 1/2 (sum of all bases) x (Height)
calculate Interest Interest (I)= principal x interest rate x time
Calculate distance traveled d = rt distance= rate x time
Calculate slope of a line (m).... (Yb -Ya)/(Xb-Xa)= m
Slope Intercept Form.. (m)=slope (b)= y-Intercept y= m(x)+b OR y= b+m(x)
Calculate midpoint on a line... (X point, y point) X point: {(Xa+Xb)/2}, y point: {(Ya + Yb)/2)}
Formula for Sum of Polygon Interior Angles...(n=# of angles) Sum of Interior angles of Polygon = 180(n-2)
Degree measurement of a single Interior Angle of regular Polygon... n=# of sides Deg. of Inter.Angle of Polygon = [180(n-2)/n]
(A) of Parallelogram=.... (A) Parallelogram = bh
Rectangular Prism: >(V)... > Surface Area ... For Rec. Prism; (V)= lwh (SA)= 2(lw) + 2(hw)+ 2(lh)
For General Prisms: V =... SA =... For General Prisms: V= (Area of Base x Height) SA= (Sum of the three faces) x 2
Right Circular Cylinder: V= SA= V= Area of Base x Height SA = 2(A of Base)+ Circumference(h)
cube Pyramid V= SA= V= 1/3(BH) = 1/3 (A of(Base))x H SA= B + (1/2 (Perim. x Slant Height))
Sphere V= SA= Sphere V= 4/3(Π)(r^3) SA= 4(Π)(r^2)
How can you use the Pythagorean Theorem when you only have degrees not points on a Right Triangle? A = Square Root of [(C ^2)-(B^2)] B= Square Root of [(C ^2)-(A^2)]
For a Triangle who has two angles of 45 deg. >Find deg. 3rd angle... & > Find Ratio of sides ... >angle 3 = 90 >Ratio of sides sides = 1,1, square root of (2)
For a Triangle who has one angle of 30 deg, another of 90 deg.. >Find deg. 3rd angle & > Find Ratio of sides = >Angle 3 = 60 deg. >Ratio of sides is: (x): (sq.rt. of 3):(2x)
if we have a right triangle with 2 sides 2 & 4.. > what is the other side & what is the Triangle ratio? > what degree ratio is the triangle? in a triangle where to side are 2, & 4,... >the final side = 2(sq.rt (3) >triangle is a 30:60:90 deg. tri.
Length of Arc= L of Arch = (L/C) = (ABC(deg)/360)
A of Arc= A of Arc = Π(r^2)
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