Geometry formulas

Question 1

Betweenness of points

Answer 1

AB+BC=AC
AB=AC-BC
BC=AC-AB

Question 2

Midpoint

Answer 2

(x1+x2 y1+y2)
_______ , ________
2 2

Question 3

Partitioning a line segment

Answer 3

(nx1+mx2 ny1+my2)
__________ , __________
n+m n+m
Where m does not equal -n

Question 4

weighted average on a number line

Weighted average on a coordinate plane

Answer 4

w1 + w2 -----------------------------------------------

   w1+w2+w3 w1y1+w2y2+w3y3 --------------------------
  w1+w2+w3

Question 5

Find missing endpoint

Answer 5

x=x1+x2 , y= y1+y2
_________ __________
2 2

Question 6

Distance Fromula

Answer 6

D= Sqrt of (x2-x1)^2 + (y2-y1)^2

Question 7

Slope

Answer 7

M= y2-y1
———
x2-x1

Question 8

Equation of a line

Answer 8

Standard: Ax + By= C
Slope Intercept: y=mx + b
Point Slope: y-y1+ m(x-x1)

Question 9

Sum of exterior angles

Answer 9

360 degrees

Question 10

One exterior angle

Answer 10

n

Question 11

Sum of interior angles

Answer 11

180(n-2)

Question 12

One interior angle

Answer 12

   n

Question 13

45-45-90 triangle

Answer 13

Hypotenuse: x Sqrt(2)
Legs: x

Question 14

30-60-90 triangle

Answer 14

Short leg: x
Long leg: x Sqrt(3)
Hypotenuse: 2x

Question 15

SOH-CAH-TOA

Answer 15

Sin A= opposite
————-
Hypotenuse
Cos A= Adjacent
—————
Hypotenuse
Tan A= opposite
————–
adjacent

Question 16

Law of sines

Answer 16

sin A sin B sin C
——– = ——– = ———
a b c

Question 17

law of cosines

Answer 17

a^2=b^2 + c^2- 2bc cos A
b^2=a^2 + c^2- 2ac cos B
c^2=b^2 + b^2- 2ab cos C

Question 18

Radius/ Diameter

Answer 18

r= d/2 d=2r

Question 19

Area of a circle

Circumference

Answer 19

A= (pi)r^2

C= 2(pi)r C= (pi)d

Question 20

Arc Length

Answer 20

S= 0/360 times 2(pi)r

Question 21

Area of a sector

Answer 21

A= 0/360 times (pi)r^2

Question 22

Equation of a circle

Answer 22

(x-h)^2 + (y-k)^2 = r^2

Question 23

Completing the square

Answer 23

(b/2)^2

Question 24

Convert degrees to radians

Convert radians to degrees

Answer 24

Multiply by (pi)/180

Multiply by 180/ (pi)

Question 25

Arc Length in radians

Answer 25

S= 0r

Question 26

Inscribed angles

Answer 26

1/2 the measure of the intersected arc

_____________________

1/2 the measure of the central angle

Question 27

Central Angle measurement

Answer 27

Same as the intercepted arc.
2 times the inscribed angle

Question 28

Angle outside of circle

Answer 28

m<exterior= greater (arc) -lesser(arc)/ 2

Question 29

Angle inside of a circle

Answer 29

m<exterior= greater (arc) + lesser(arc) /2

Question 30

Segments of intersecting chords

Answer 30

a(b) = c(d)

Question 31

Segments of intersecting secants

Answer 31

x(x+y) = w(w+z)

Question 32

Segments tangent/ Secant intersecting

Answer 32

x^2 = w=(w+z)

Question 33

segments of intersecting tangents

Answer 33

a=b

Question 34

prisms

Answer 34

Volume: V= Bh
Surface Area: SA= Ph + 2B

Question 35

Cylider

Answer 35

Volume: V=Bh
Surface Area: SA= Ph +2b

Question 36

Central Angle

Answer 36

360/n

Question 37

Diagonals, number of

Answer 37

n(n-3)/2

Question 38

Area of rectangle

Answer 38

A = l x w

Question 39

Area of a trapezoid

Answer 39

A= b1 + b2
—————- x h
2

Question 40

Area of a square

Answer 40

A= s^2

Question 41

Area of a parallelogram

Answer 41

A=bh

Question 42

Area of a rhombus/ kite

Answer 42

A= d1+d2
———–
2

Question 43

Area of a regular polygon

Answer 43

A= 1/2 aP

Question 44

Area of a triangle

Answer 44

A- bh /2

Question 45

Similar right traingle

Answer 45

Altitude x = Sqrt (ab)
short leg: d= Sqrt (ac)
long leg: e= Sqrt (bc)

Question 46

Pythagorean Theorem

Answer 46

a^2 + b^2 = c^2