1. *SEGMENTS AND RAYS* x= 180 – 50
ABCDEFGHIJ x = 130
-2 -1 0 1 2 3 4 5 6 7 -Complementary Angle-
BH = /B-H/
= /-1-5/
=6 Let x = the other angle
x + 65 = 90
*FINDING THE MIDPOINT
BETWEEN K&B* x = 90 – 65
K B x = 25
-8 15 -Vertical Angles-
Let m= midpoint between KB J X
Z 2x + 75 P
m= a+b
2
Find x:
= -8+ 15
2x+75+x= 180
2
2x+x= 180- 75
=7
3x = 105
2
3 3
m= 3. 5
X= 35
*SPECIAL ANGLES &
ANGLE PAIR* Find ZAP
ZAP= 2X+75
-Supplementary Angles-
ZAP= 2(35)+75
ZAP= 70+75
ZAP= 145
Let x = is the 1st angle
JAZ = XAP is 35 ZAP=JAX is 145.
x +50 = 180
2. *POLYGONS* -Finding the measures of each interior
angles-
-Diagonals-
I= 180(n-2)
n = vertices of polygon
n
d = n(n-3)
-For hexagon-
2
I= 180(n-2)
-For Nonagon-
n
d = n(n-3)
I= 180(6-2)
2
6
= 9(9-3)
I= 180(4)
2
6
= 9(6)
I= 720
2
6
= 54
I= 120
2
*MEASURES OF PLANE
= 14
FIGURES AND GEOMETRIC
-Finding the sum of all interior angle- SOLIDS*
S = 180(n-2)
-Perimeter of Polygonal Regions &
-For Pentagon- Circumference of a Circle-
S= 180(n-2) -Perimeter of a triangle-
S= 180(5-2) P= a + b + c
S= 180(3)
S= 540 A 16 B 58 P= a + b + c
= 16+58+64
C 64 P= 138
3. -Perimeter of a square- -Finding the Radius-
P= 4s s= 18 r=
s s
If C= 8.75 cm
s s
r =?
P= 4s
r=
P= 4(18)
r=
P= 72
r = 1.38 cm
-Perimeter of a Triangle-
P= 2L+2W *AREAS OF POLYGONAL
L= 16, W=8 L
REGIONS AND CIRCLES*
-Rectangle & square-
W w
Area of a rectangle
A = lw
L
If L =10
P= 2L+2W
W=5
P=2(16)+2(8)
A= lw
P= 32+16
A= 10(5)
P= 48
A= 50
-Circumference-
Area of a square
C= 2πr
π = 3.1416
-Parallelograms’ and Triangles-
If r = 86 cm Area of Parallelograms
C= 2πr A= bh
= 2(3.1416)(86) If b = 8, h =10
= 2(270.1776) A= bh
C= 540.3552 A= 8(10) =80
4. Area of the triangle Volume of a prism
V= Bh
A=
B= 660 sq units, h = 25
-Rhombus and Trapezoid- V=Bh
Area of the Rhombus V= 660(25)
A= V= 16,500
Lateral area of a right cylinder
Area of the trapezoid
S= 2πrh
)
Total Surface area of a right cylinder
T= 2πr(h+r)
-Area of a Circle- Volume of a cylinder
V= π h
*VOLUMES AND AREAS OF -Pyramid & Cones-
SOME GEOMETRIC SOLIDS* Lateral Area of a regular pyramid
- Prism and cylinders- S= hP
Area of a Prism Total surface Area of a regular pyramid
S= Ph
T= hP+B
For regular hexagonal prism
Volume of a Pyramid
If h =15, P= 6 x 3
V= Bh
S=Ph
Volume of a rectangular solid
S= (6 x 3) (15)
V= lwH
S= 270 sq units
Total surface area of a right prism *THE ANGLES OF
T= Ph+2b TRIANGLES AND
QUADRILATERALS*
-Interior and Exterior Angles of an n-gon-
5. (n-2)180= sum of the measures of the interior Major arc (360) = the measure of
angles of a polygonal n-sides
corresponding minor arc
*ISOSCELES AND Inscribe angle = intercepted arc
OVERLAPPING
2
TRIANGLE*
*THE PLANE
30-60-90
COORDINATE
GEOMETRY*
c =2b *REVIEW OF THE CARTESIAN
45-45-90 COORDINATE SYSTEM*
The Distance Formula
*SIMILAR TRIANGLES*
Midpoint formula
=cx
Lines
x = c-y
c = x+y
y = c-x Circles
*THE PYTHAGOREAN An equation of the circle w/
THEOREM* center (h,k) and radius r is
*ANGLES,ARCS, AND
CHORDS*
