Download Geometry

 23


questions
14 plane geometry
9 coordinate geometry
 No
proofs, theorems
 Common formulas and questions
 Most drawings are actually drawn to scale
 Easier to do process of elimination
 If there is no drawing and you are confused
draw one
 Angles
and lines
 Triangles
 Quadrilaterals
 Circles
 Lines
form angles of 180˚
 Two intersecting lines make four angles but
they only have two different measures
 Two lines cut by a transversal make 8 angles
but they still only have two different
measures


Vertical angles are opposite each other and are
equal
Supplementary angles add up to equal
180˚(linear pair)
 Three
sided figure
 Sum of interior angles is 180˚
 Isosceles triangle = two sides of equal length
 Equilateral triangle = all sides and angles of
equal measure
 Right triangle = one angle of the triangle is
90˚
 Pythagorean Theorem = a2 + b2 = c2
 Pythagorean triple = three numbers that
solve the Pythagorean theorem
 Area of a triangle = A = ½ bh
 3,
4, 5
 5, 12, 13
 7, 24, 25

Any multiples of these
 Isosceles

right triangles
Angles are 45˚-45˚-90˚, sides are in the ratio
1:1:√2 or x:x:x√2
 30˚-60˚-90˚triangles

Angles are 30˚-60˚-90˚, sides are in the ratio
1:√3:2 or x:x√3:2x
 Angle
measures are the same
 Sides are proportional
 Set up proportions to find the missing sides
 Four
sided figures, sum of interior angles is
360˚
 Square = four equal sides, four right angles

A = s2, P = 4s
 Rectangle

= four right angles
A = lw, P = 2l +2w
 Parallelogram

A = bh, P =2b +2h
 Trapezoid

= two pairs of parallel sides
= one pair of parallel sides
A = ½ h(b1+b2)
 Radius
= distance from the center of the
circle any point on the circle
 Diameter = distance from one point on the
circle to another going through the center
 Chord = line segment connecting two points
on the circle that does not go through the
center
 Tangent = line that only touches the circle in
one distinct spot
 Circumference = distance around, C = 2πr
 Area = A = πr2
 Graphing!!!!!!!!!


Number-lines, inequalities
Graphing on a coordinate plane
 Graphing




inequalities on a number line
Solve the equation as if there is an equal sign.
If there is an equal to line under the inequality
sign, there will be an closed or filled in circle
If there is no equal to line under the inequality
sign, the circle is open.
A solid line denotes which numbers are solutions
to the problem
 Cartesian
grid or plane
 Few actual graphing questions on ACT, mostly
you will use graphs to answer questions
 Use process of elimination to narrow down


Is the answer in the right quadrant?
Could the point be on the line?
 Slope
intercept or Y-intercept formula
 Slope formula
 Midpoint formula
 Distance Formula
 Circles
 Ellipses
 Parabolas
 y=mx+b


m is the slope
b is the y intercept
(y1-y2)
 m= ---------
(x1-x2)

 x1+x2/2,

y1+y2/2
d
= √((x2-x1)2+(y2-y1)2
 (x-h)2+(y-k)2=r2
 Center
of the circle is (h,k)
 r is the radius
 (x-h)2+(y-k)2


----a2
 Center
----- =1
b2
of the ellipse (h, k)
 2a = horizontal axis width
 2b = vertical axis width
 y=x2
 They
will give you a standard formula and
ask you to put it into slope intercept
 They will give you points and ask you to find
slope
 Find midpoints given two coordinates or find
the missing coordinate if you know one and
the midpoint
 Find distance between points
 They will give you an equation and ask you
what shape it will be when graphed
 You
can graph most of these on your
calculator to solve
 Or you can estimate most of them
 Worksheets