regents geometry mc and review

Question 1

finding area/perimeter for triangles

Answer 1

1) use perimeter/area of whatever particular shape ex. A = s2 and P= 4s for a square, for a parallelogram/rhombus/rectangle Area= bh Perimeter= 2b+ 2h
2) use distance formula (for triangles, use it for the sides that isn’t the base or height)
3)

Question 2

reflecting a shape over a particular line
ex. triangle ABC, with vertices A (0,0) B (3,5), C (0,5) is graphed, what is its height and radius length when reflected?

Answer 2

be wary of which line of the shape is being reflected and take into consideration how the new perspectiv of the 3-d shape changes the height/radius length (they switch often with the way the shape faces)

Question 3

centroid

Answer 3

2/3rds distance from each vertex from their midpoints from each side,
point of concurrency for the medians

Question 4

How to find altitude (slope of line, flipped and negated, with vertex of triangle)

Answer 4

1) find slope of the side the altitude intersects and flip & negate it
2) Use the vertex (where altitude begins) and the slope to set up an equation

Question 5

How to find median (random pair of coordinates from line with slope, made up from vertex & midpoint of that line)

Answer 5

1) find MIDPOINT!!!! of the line the median intersects
2) take those coordinates + the vertex’s coordinates to find slope of the median
3) use THIS SLOPE and a RANDOM pair of coordinates from the line to set up the equation

Question 6

proportion problems

Answer 6

BE CAREFUL of where the numbers are, make sure your proportion ise evenly set up

Question 7

reflections

Answer 7

positive reflection is clockwise, negative reflection is counterclockwise

Question 8

a rigid motion is a transformation in which the pre image and image are

Answer 8

congruent

Question 9

the rigid motion transformations (preserving distance and angle measure)

Answer 9

reflection, rotation, translation

Question 10

reflection

Answer 10

image and pre image will have opposite orientations, they will have different orientations with an odd amount of reflections/single flip and the same orientations with an even #

Question 11

reflection over x axis (x,y)

Answer 11

(x,-y)

Question 12

reflection over y axis (x,y)

Answer 12

(-x, y)

Question 13

reflected over y= x (x,y)

Answer 13

(-y, x)

Question 14

reflected over -y=-x

Answer 14

(-y,-x)

Question 15

positive rotation

Answer 15

clockwise

Question 16

negative rotation

Answer 16

counterclockwise

Question 17

when applying transformations

Answer 17

apply the 2nd one first

Question 18

glide reflection

Answer 18

reflection + translation

Question 19

invariant point

Answer 19

image has the same coordinates as the original point under a transformation

Question 20

congruency transformation

Answer 20

pre image and image are congruent

Question 21

similarity transformation

Answer 21

pre image and image are similar

Question 22

dilation

Answer 22

1) plug in equation on calculator and search for center point that the line is supposed to be dilated by
2) if it is there, nothing changes. if it isn’t, it’s parallel so the slope doesn’t change but the y-intercept does.

Question 23

how to tell if a shape carries onto itself

Answer 23

envision it/draw it and preform the transformation to see if the shape looks the same

Question 24

Rectangle A’ B’ C’ D’ is the image of rectangle ABCD after a dilation centered at point A by a scale factor of 2/3rds so

Answer 24

perimeter is in the same ratio as the sides, area is the square of the ratio of its sides so A’ B’ C’ D’ has the perimeter that is 2/3rds the perimeter of rectangle ABCD

Question 25

Area of a triangle on coordinate geometry

Answer 25

0.5 (1/2) (x1 (y2-y3) + x2 (y3-y1) + x3 (y1-y2)

Question 26

altitude

Answer 26

works as height when solving for area of a triangle on a coordinate

Question 27

area of a sector

Answer 27

x/360 pi (r) 2

Question 28

area of arc length

Answer 28

x/360 x 2(pi)(r)

Question 29

median

Answer 29

goes to midpoint of the opposite side (perpendicular bisectors technically do this too which is why they classify as such and the triangles wind up isosceles with reflexive and 1/2 of each base

Question 30

if a composition of trnasformations includes a dilation

Answer 30

the transformation is similar

Question 31

a composition of line reflections over 2 parallel lines (or any even # of II lines) are equal to

Answer 31

a translation

Question 32

a composition of line reflections over 3 II lines (or any odd # of II lines) is equivalent to

Answer 32

a single reflection

Question 33

how to rotate/dilate a figure about a center than the origin

Answer 33

1) translate the center of rotation to the origin
2) apply that translation to the points of the actual figure and then translate back

Question 34

translations/dilations of circles can prove that

Answer 34

all circles are similar

Question 35

equation of a horizontal line

Answer 35

y = #

Question 36

equation of a vertical line

Answer 36

x = #

Question 37

triangle angle sum theorem

Answer 37

<1 + <2 + <3 = 180

Question 38

exterior angle sum theorem

Answer 38

<1 + <2 + < 4

Question 39

circumcenter

Answer 39

point of concurrency between the perpendicular bisectors, can be outside, inside, or on the triangle, if the triangle is right it lies on the midpoint of the hypotenuse

Question 40

incenter

Answer 40

point of concurrency between the angle bisectors, will always be inside the circle

Question 41

orthocenter

Answer 41

point of concurrency between the altitudes of each triangles

Question 42

if the triangle is acute, the circumcenter and orthocenter are inside the triangle, if it is obtuse, they are outside the triangle, if it’s right the circumcenter is on the midpoint of the hypotenuse, and the orthocenter is on the vertex of the right angle

Question 43

in a triangle, the third side must be more than the difference of the two sides but less than the sum of the other two sides

Question 44

the shortest side is opposite to the smallest angle, the longest side is opposite to the longest angle

Question 45

when finding angles for a inscribed quadrilateral –> opposite angles

Question 46

seg 1 /a = a /seg 2, leg/h = h/leg projection