Geometry Regents Reveiw

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 Author: MissCoppola ID: 156782 Filename: Geometry Regents Reveiw Updated: 2012-06-06 09:39:08 Tags: Geometry Math Review Folders: Description: Review for the Geometry Regents Show Answers:

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1. 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!
2. Equation of a circle (MEMORIZE THISS!)

• where (h, k) is the center
3. 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.
4. 5 ways to prove congruent triangles
• SSS
• SAS
• AAS
• ASA
• HL (need to prove right triangles first)

Can't use A.A.A or ASS!!

5. How do you find the length of the altitude in the diagram above?
6. Sum of Interior angles of Any Polygon
180(number of sides-2)
7. Sum of exterior angles in any polygon
8. How do you find the measure of ONE EXTERIOR ANGLE of a polygon
360/number of sides
9. How many degrees is EACH angle in an equilateral triangle
60 degrees
10. What are things we know about rhombi?
all sides CONGRUENT

Diagonals are perpendicular

Diagonals bisect the angles

It is a special parallelogram
11. 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
12. 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.
13. What must be true about the side lenghts of a triangle...

E.X: Which of the following lengths can create a triangle?

a) {3,6,2}
b) {3,6,8}
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!
14. 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
15. HOW can you prove triangles are SIMILAR (~)
• AA~
• SAS~
• SSS~

(the S in this case meas CORRESPONDING sides are PROPORTIONAL)
16. Angles/ Side lenghts in triangles

Smallest side opposite smallest angle

Largest side opposite largest angle
17. What is the locus of points that are a fixed distance from a point "P"?
THINK BRAD AND HIS LIZARD ON A LEASH!!
18. DISTANCE FORMULA
19. Midpoint formula

or

(average the x's, average the y's)

MAKE SURE IT MAKES SENSE BY GRAPHING IT
20. What is an isometry?
a transformation that PRESERVES SIZE

the only transformation that is NOT an isometry is a Dilation!
21. Inverse
Negate
22. Converse
Flip

(you can do FLIPS IN CONVERSE SNEAKERS)
23. CONTRAPOSITIVE
Logically equivalent to the original

FLIP AND NEGATE
24. What is a glide reflection?
It is a transformation that combines a TRANSLATION (glide) and a REFLECTION
25. Area of a Circle!
A = pi*r2
26. Area of a triangle
27. Area of a Trapezoid
• or

A = (average of the bases times the height)
28. What do we know about the slopes of PARALLEL LINES?
THEY ARE THE SAME!
29. 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
30. 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.
31. How many degrees are in ANY quadrilateral?
360
32. Supplementary
33. Complimentary Angles
34. Linear Pair
Two angles who create a line (they add to 180)
35. What does bisect mean?
To cut in half

(makes two EQUAL pieces)
36. Similar Right Triangls

How do you find the length of the altitude in the diagram.
• in this case
37. 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!
38. What is the locus of points equidistant from a POINT?
THINK BRAD WITH HIS LIZARD ON THE LEASH! (it makes a circle!!!)
39. What is the locus of points equidistant from a single line?
Two lines that run parallel to it
40. What is the locus of points equdistant from two points?
The PERPENDICULAR BISECTOR of the segment that connects them.

41. What is the point of concurrency for the perpendicular bisectors of a triangle?
Circumcenter
42. What s the point of concurrency for the ANGLE bisectors of a tangle
INCENTER

this point is EQUIDISTANT from the sides of a triangle
43. What is a median of a triangle?
It connects the vertex of a triangle to the midpoint of the opposite side
44. What is the Point of concurrency of the MEDIANS of a triangle
• Centroid!
• Important

• Pieces are in the 2:1 Ratio
• (2x + x = median length)
45. What do we know about Central Angles in a circle

< = intercepted arc

46. What do we know about INSCRIBED ANGLES?
• < = 1/2(arc)
47. How do you find the valu of x in the diagram below?

x = 1/2 (sum of the arcs)
48. How do you find the measure of angles outside a circle, formed by two tangents or secats?
49. How do you find the measure of <1
<1 is half Arc AB

< 1 = 65
50. What do you know about angles in the polygon below?

<E + <G = 180
51. What is the equation of a LINE?
y = mx + b

• Where m is the SLOPE and
• b is the y intercept!
• FH = DH

• and Arc FG = Arc GD
• and Arc ED = Arc EF
53. What euation can we use to find the lengths of the chords in the diagram below?
• piece*piece = piece*piece
54. What equation can we use to find lenghts in this diagram?
External * Whole = External * Whole
55. Identify the two congruent chords in the diagram below
• Arc AB = Arc CD
56. What is the "Rotation Table"

(set up this table the second you get your test!!)
57. How do you reflect over the line y = x
FLIP THE X AND Y COORDINATE
58. Exterior < theorem
How do you find he measure of <1
• <1 = <B + <A
59. What do we know about the length of MIDSEGMENT BE?
• BE = 1/2 (CD)

BE || CD
60. What do we know about midsegent GJ?

or GJ = Average of the bases!
61. What are some true proportions you can set up based on this diagram

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