Geometry

Question 1

Three Rules to Live by in Geometry

Answer 1

1) If they don’t tell you, don’t assume.
2) If they give you something, use it.
3) Know rules and formulas

Question 2

Inscribed means

Answer 2

lies inside and vertices touch the other shape; indicates relationships between them

Question 3

Area of a square

Answer 3

s^2

Question 4

Area of a rectangle

Answer 4

L x W

Question 5

Area of a triangle

Answer 5

1/2bxh

Question 6

What is height in a triangle

Answer 6

Perpendicular line from base to the top of the triangle in reference to that base (base can be any of the three sides)

Question 7

Area of a trapezoid

Answer 7

((b1 + b2) / 2) x h

Question 8

Area of a parallelogram

Answer 8

b x h (need to find height)

Question 9

Perimeter of square

Answer 9

4 s

Question 10

Perimter of rectangle

Answer 10

2L + 2W

Question 11

Perimeter of a triangle

Answer 11

x + y + z (all sides added up)

Question 12

Perimeter of a parallelogram

Answer 12

2L + 2W

Question 13

Area of a circle

Answer 13

πr^2

Question 14

Circumference of a circle

Answer 14

2πr or πd

Question 15

Area of a sector

Answer 15

find Area of sector as a percentage of area of circle (ratio of angles will tell you this), then solve after know something about area of circle

Question 16

Arc length

Answer 16

Length of circumference; must find circumference and then relate amount of arc as sector of circle (using angles) and determine what portion it represents

Question 17

Central angle

Answer 17

Vertex of a central angle is the center

Question 18

Inscribed Angle

Answer 18

One shape within another, where vertices touch on edge of shape

Question 19

If Inscribed triangle has hypotenuse as diameter…

Answer 19

is a right triangle

Question 20

Relationship of central angle to inscribed angle (sectors)

Answer 20

central angle is 2x relative to the inscribed angle with the same end points.

Question 21

Special Right Triangles

Answer 21

45-45-90

30-60-90

Question 22

45-45-90 Triangle side length relationships

Answer 22

x (leg), x (leg), x√2 (hypotenuse)

Question 23

30-60-90 Triangle side length relationships

Answer 23

x (shorter leg), x√3 (longer leg), 2x (hypotenuse)

Question 24

Equilateral Triangle

Answer 24

All sides of equal length, angels are 60 each

Question 25

Isosceles Triangle

Answer 25

Two sides and two angles are even

Question 26

Pythagorean Triples

Answer 26

3-4-5 6-8-10 (or other multiples of 3-4-5) 5-12-13 (or 10-24-26) 8-15-17

Question 27

Similar Triangles

Answer 27

Triangles with same angles have proportionate sides

Question 28

Relationship of angles and sides

Answer 28

Angle size corresponds to side length size (referring to the side length opposite the angle

Question 29

Volume of a 3D rectangular shape

Answer 29

l x w x h

Question 30

Surface area of a 3D rectangular shape

Answer 30

2 x (LxW + LxH + WxH)

Question 31

Volume of a cube

Answer 31

s^3

Question 32

Surface Area of a cube

Answer 32

6s^2

Question 33

Volume of a cylinder

Answer 33

πr^2h

Question 34

Surface Area of a cylinder

Answer 34

2(πr^2) + 2πrh

Question 35

Slope

Answer 35

Rise over Run | y1 - y2 over x1-x2

Question 36

Intersecting Lines Rules

Answer 36

Interior angles add to 360° Interior angles that combine to form a line sum to 180° Angles found opposite each other where two lines intersect are equal (vertical angles)

Question 37

Parallel Lines cut by a transveral rules

Answer 37

Watch for this to be disguised (remember the Z) Eight angles are formed, but there are only 2 distinct angles; draw and label them a° and b°; a + b = 180 A is the acute less than 90°; B is the obtuse greater than 90°

Question 38

Polygon Sum of Interior Angles

Answer 38

(n-2) x 180°

Question 39

Length range of third side of a triangle

Answer 39

sides are a b c | b-a

Question 40

Exterior Angles of a Triangle

Answer 40

Exterior angle is equal to the sum of the two non-adjacent interior angles of the triangle

Question 41

Circle Radius, Diamter, Circumference and Area

Answer 41

Know one value, can figure the rest

Question 42

Describe 4 quadrants, counterclockwise (coordinate plane)

Answer 42

``` Quad 1 upper right hand corner (positive y, positive x) Quad 2 (Positive y, negative x) Quad 3 (negative y, negative x) Quad 4 (negative y, positive x) ```

Question 43

Vertical line slope | Horizontal line slope

Answer 43

x = 0 (or some other number) (undefined) (vertical line) y = 0 (or some other number) slope is 0 (horizontal line)

Question 44

Area of rhombus

Answer 44

(Diagnol 1 x Diagnol 2)/2

Question 45

Max area of a quadrilateral

Answer 45

closest to square

Question 46

Minimum perimeter

Answer 46

square

Question 47

Sector calculations

Answer 47

Central angle / 360, sector area / circle area, and arc length / circumference

Question 48

Parallelogram diagnols

Answer 48

Make equal triangles, cut angles in half, bisect each other

Question 49

Geometry process

Answer 49

1) draw or redraw figures, fill in all given info, identify target 2) identify relationships and create equations 3) solve equations for missing value 4) Make inferences from figures

Question 50

Perimeter of a sector

Answer 50

2r + arc length

Question 51

Similar shapes have sides in ratio a:b, have areas in ratio...

Answer 51

a^2 : b^2

Question 52

Maximize area of a polygon for given perimeter

Answer 52

Make side lengths as close to equal as possible

Question 53

Minimize perimeter for given area of a polygon

Answer 53

Make sides as close to equal as possible

Question 54

Maximize area of a triangle or parallelogram

Answer 54

Put known sides perpendicular to each other

Question 55

A of an equilateral triangle

Answer 55

(s^2sqrt3)/4

Question 56

Diagnol of cube

Answer 56

s* sqrt 3

Question 57

Slope of perpendicular bisectors

Answer 57

Negative reciprocal

Question 58

Point of intersection of bisector

Answer 58

X = average of x coordinates Y = average of y coordinates

Question 59

Point of intersection of two lines

Answer 59

Point solves two equations - solve as a system of equations If parallel lines, never intersect If same line in different forms, will intersect infinitely at every point

Question 60

Characteristics of quadratic function graphs f(x)=ax^2 + bx + c

Answer 60

a>0, curve opens up | a

Question 61

How many times will a quadratic graph touch x axis? How solve for these?

Answer 61

Find by plugging points Solve the quadratic - factoring Use discriminat b^2 - 4ac, use quadratic formula