Geometry Regents Reveiw
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Conjunction (And Statements)
Squares are parallelograms and trapezoids are circles
BOTH PARTS must be true to be true
T and F therefore the statement is false!
Equation of a circle (MEMORIZE THISS!)
- where (h, k) is the center
- r = radius
Disjunction (or Statements)
Squares are parallelograms OR trapezoids are circles.
One piece needs to be true for this to be true
T or F therefore the statement is TRUE.
5 ways to prove congruent triangles
- HL (need to prove right triangles first)
Can't use A.A.A or ASS!!
How do you find the length of the altitude in the diagram above?
Sum of Interior angles of Any Polygon
180(number of sides-2)
Sum of exterior angles in any polygon
ALWAYS ADDS TO 360
How do you find the measure of ONE EXTERIOR ANGLE of a polygon
360/number of sides
How many degrees is EACH angle in an equilateral triangle
What are things we know about rhombi?
all sides CONGRUENT
Diagonals are perpendicular
Diagonals bisect the angles
It is a special parallelogram
What do we know about squares?
they have all the proprties of a rectangle and a rhombus. Most importantly:
- 90 DEGREE ANGLES
- DIAGONALS ARE PERPENDICULAR
- Diagonals are CONGRUENT
- All sides are congruent
How do you prove something is a TRAPEZOID on a coordinate grid?
It has one pair of parallel sides.
It has one pair of NON PARALLEL SIDES.
What must be true about the side lenghts of a triangle...
E.X: Which of the following lengths can create a triangle?
The sum of the two smaller sides must be larger than the longest side!
3 + 2 is less than 6 (so A wont make a triangle)
choice B will make a triangle!
What do we know about SIMILAR FIGURES?
Corresponding ANGLES are CONGRUENT
Ratio of sides = ratio of perimeters = ratio of altitudes
- (Ratio of sides)2= ratio of areas
- (ratio of sides)3= ratio of volumes
HOW can you prove triangles are SIMILAR (~)
(the S in this case meas CORRESPONDING sides are PROPORTIONAL)
Angles/ Side lenghts in triangles
Smallest side opposite smallest angle
Largest side opposite largest angle
What is the locus of points that are a fixed distance from a point "P"?
THINK BRAD AND HIS LIZARD ON A LEASH!!
(average the x's, average the y's)
MAKE SURE IT MAKES SENSE BY GRAPHING IT
What is an isometry?
a transformation that PRESERVES SIZE
the only transformation that is NOT an isometry is a Dilation!
(you can do FLIPS IN CONVERSE SNEAKERS)
Logically equivalent to the original
FLIP AND NEGATE
What is a glide reflection?
It is a transformation that combines a TRANSLATION (glide) and a REFLECTION
Area of a Circle!
A = pi*r2
Area of a Trapezoid
A = (average of the bases times the height)
What do we know about the slopes of PARALLEL LINES?
THEY ARE THE SAME!
What do we know about the slopes of PERPENDICULAR LINES?
negative reciprocals (flip and change sign)
for example a line with m=2 is perpendicular to a line with a slope of m=-1/2
What is the Lateral Area of a Cone or a Cylinder?
It is the "wrapper". It does not include the bases.
The Lateral area formulas for BOTH the cone and the Cylinder are on your reference table.
Note: To get the complete surface area you must add on the bases.
How many degrees are in ANY quadrilateral?
Adds to 180 degrees
adds to 90
Two angles who create a line (they add to 180)
What does bisect mean?
To cut in half
(makes two EQUAL pieces)
Similar Right Triangls
How do you find the length of the altitude in the diagram.
How do you solve a system of equations graphically?
- 1. Solve both equations for y.
- 2. Graph them on your graphing calculator and use your table to graph them on the coordinate grid.
- 3. Locate the points of intersection, circle them and then RECORD THEM!
What is the locus of points equidistant from a POINT?
THINK BRAD WITH HIS LIZARD ON THE LEASH! (it makes a circle!!!)
What is the locus of points equidistant from a single line?
Two lines that run parallel to it
What is the locus of points equdistant from two points?
The PERPENDICULAR BISECTOR of the segment that connects them.
What is the point of concurrency for the perpendicular bisectors of a triangle?
What s the point of concurrency for the ANGLE bisectors of a tangle
this point is EQUIDISTANT from the sides of a triangle
What is a median of a triangle?
It connects the vertex of a triangle to the midpoint of the opposite side
What is the Point of concurrency of the MEDIANS of a triangle
- Pieces are in the 2:1 Ratio
- (2x + x = median length)
What do we know about Central Angles in a circle
< = intercepted arc
What do we know about INSCRIBED ANGLES?
- < = 1/2(arc)
How do you find the valu of x in the diagram below?
x = 1/2 (sum of the arcs)
How do you find the measure of angles outside a circle, formed by two tangents or secats?
How do you find the measure of <1
<1 is half Arc AB
< 1 = 65
What do you know about angles in the polygon below?
Opposite angles add to 180
<E + <G = 180
What is the equation of a LINE?
y = mx + b
- Where m is the SLOPE and
- b is the y intercept!
What do we know about this picture?
- FH = DH
- and Arc FG = Arc GD
- and Arc ED = Arc EF
What euation can we use to find the lengths of the chords in the diagram below?
- piece*piece = piece*piece
What equation can we use to find lenghts in this diagram?
External * Whole = External * Whole
Identify the two congruent chords in the diagram below
- Arc AB = Arc CD
What is the "Rotation Table"
(set up this table the second you get your test!!)
How do you reflect over the line y = x
FLIP THE X AND Y COORDINATE
Exterior < theorem
How do you find he measure of <1
- <1 = <B + <A
What do we know about the length of MIDSEGMENT BE?
- BE = 1/2 (CD)
BE || CD
What do we know about midsegent GJ?
or GJ = Average of the bases!
What are some true proportions you can set up based on this diagram
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