Download geometry journal 1

POINT,LINE AND PLANE
Point: A single dot in space, used to describe location. It is
described with a dot and a capital letter.
P
Line: A straight connection of points that goes on forever in both
directions.
XY
YX
Plane: A flat surface that goes on forever, it has no thickness and
it contains 3 points.
T
COLLINEAR AND COPLANAR POINTS

The difference between collinear and coplanar
points is collinear points coexist in in the same
line and coplanar points coexist in the same
plane.
Collinear
Coplanar:
P
N
A
B
M
COLLINEAR AND COPLANAR POINTS
Collinear Counterexapmple
Coplanar Counterexample
LINE, SEGMENT, AND RAY
Line: A straight connection of points that goes on forever in both
directions.
XY
YX
Segment: Any straight collection of dots that has a beginning and
an end (endpoints)
XY
Ray: A straight collection of points that has one end point and
goes on forever.
XY
*This are related because they all are ways to use points and
lines, also we will be using them for the rest of the school year.
Besides their everyday location and distance applications.
INTERSECTION OF LINES AND PLANES

It is when two lines intersect through the same line in
any situation. Like in Postulates 1-1-4 (If two lines
intersect, then they intersect in exactly one point) and
1-1-5 (If two planes intersect, then they intersect in
exactly one line)
POSTULATE, AXIOM AND THEOREM

The Difference between Postulate, Axiom and Theorem is
between Postulate and Axiom is nothing they are
interchangeable terms (this are accepted truths as fact with out
proof), but between this and theorem is that a theorem is a
theoretical proposition, later to be proved by other propositions
and formulas.
RULER POSTULATE (POSTULATE 1-2-1)





To measure segments use a ruler and just subtract
the values at the end points.
A Field is 120 ft long and a player starts running from 60 ft , what is the
distance when he runs to point 120 ft?
Answer: 60 ft,
The road is 130km long and a car starts its trip from south park which is
90km up the road, when he reaches the 130 km line how many km does
the car have traveled? Answer: 40km
The sidewalk is 850mt long and an old lady starts walking from 500mt,
when she reaches the end of the sidewalk, what’s her current distance
Answer: 350mt.
SEGMENT ADDITION POSTULATE (1-2-2)

If A,B,C (our three collinear points) and B is between A
& C, then AB+BC=AC
24

C


A
so CA+AB= CB
72
A
B
so AB+BC=AC
75
E
F
so EF+FG=EG
46
B
24+46= 70, so CB = 70
C
72+20= 92, so AC = 92
20
55
G 75+55= 130, so EG = 130
DISTANCE BETWEEN TWO POINTS ON A COORDINATE PLANE
 To find the distance between two points on a coordinate plane

you have to take the X1 and X2 coordinates and square them
then the Y1 & Y2 coordinates and do the same, add and then
square the answer. d = √ (X₁-X₂)₂+(Y₁ -Y₂)₂
AB= √(5-0)₂+(1-3)₂ * CD= √(-3 –(-1)₂+(-4 - 1)₂
√5₂ + (-2)₂
√(-2)₂+(-5)₂
√25+ 4
√ 4+25
This are congruent
√29
√29
d= √(4-1)₂+(2-6)₂
√3₂+(-4)₂
√9+16
√25 = 5
this is a random problem
CONGRUENCE AND EQUALITY

Congruence means and equal measure, not necessarily a
value, we are comparing names; this contrasts with
equality because that means 2 things with same value,
therefore it is comparing values. They are similar because
both are comparing two things. They are different because
congruent is two objects exactly the same regardless of
orientation, and equality is shape size and angles, like two
squares they are congruent but don’t have measurements
meaning we don’t know if they are equal.
≈
=
PYTHAGOREAN THEOREM (THEOREM 1-6-1)

In a right triangle, the sum of the squares of the
lengths of the legs is equal to the square of the length
of the hypotenuse. a₂+b₂=c₂

a=4 and b=5
c₂= a₂+b₂
=4₂+5₂
=16+25
=41
c=√41
c≈ 6.4
a=3 and b=4 find the value of c
c₂= a₂+b₂
a₂+b₂=c₂ a=4 b=5
= 3₂+4₂
4₂+5₂= c₂
=9+16
16+25= c₂
=25
41= c₂
c=√25
c≈ 5
ANGLES

Angles are 2 rays that share a common end
point. There are acute (smaller than 90°), right
(90°), obtuse (bigger than 90°) and finally
straight angles (180°)
Right Acute Obtuse Straight
Exterior Interior
ANGLE ADDITION POSTULATE (1-3-2)

2 small angles add up to the big angle.
1.angle ABD=150 2.angle EFI=180 3.angle VXY=110
angle ABC=45
angle FGI=90
angle YXZ=60
150-45=
180-90=
110+60=
CBD=105
EFG=90
VXY=170
MIDPOINT (CONSTRUCTION AND MIDPOINT FORMULA)

Midpoint is what we call the middle of the segment,
equidistant from the endpoints; cuts into two equal smaller
segments. To construct a midpoint first draw a segment,
second draw a line a little bit passed the approximate middle,
third draw two arcs from both endpoints in the two sides of the
segment, fourth draw a straight line through the crossings and
you have your constructed midpoint.
MIDPOINT FORMULA: (X₁+X₂/2,Y₁+Y₂/2)
1.(6+4)(4+1)/2 m=1.5
2.(-3+0)(-1,1)/2 m=-1.5
3. (-3+-1.5)(4+1)/2 m= -.75,2.5
ANGLE BISECTOR (CONSTRUCTION)

An angle bisector is a line which cuts and angle into
two equal parts, therefore the word bisect means to
cut in have. First lock your compass, make an arc in
each side put the point in each arc and make an arc in
the interior; then connect the vertex to the intersection
point.
ADJACENT, VERTICAL AND LINEAR PAIRS
Adjacent: are 2 angles that have the same vertex and a same
side.
 Linear Pairs of Angles: 2 adjacent straight angles that will form
a straight line. Meaning all Linear Pairs of Angles are
supplementary (Linear Pair Postulate, L.P.P)
 Vertical: Non adjacent angles formed when 2 lines intersect;
vertical angles are always congruent.
Adjacent:
Linear Pairs:
Vertical:

COMPLEMENTARY AND SUPPLEMENTARY


Complementary angles are 2 angles that add up to
90º and supplementary add up to 180º;
supplementary are always linear pairs but
complementary aren`t, they are always adjacent.
Complementary: 90º
Supplementary: 180º
PERIMETER AND AREA
Square: to take the perimeter of a square add all 4 sides
(P=4s) and area just square one side (A=s₂)
 Rectangle: to take the perimeter of a rectangle add the 2
lengths and 2 widths (P=2l+2w) and area multiply length time
width (A=lw)
 Triangle: to take the perimeter of a triangle (a+b+c) and to take
the area (bh/2)
Square:
P=4(4), P=16ft. Rectangle: 5ft.
4ft. A=4₂, A= 16ft₂
4ft.

P=5+5+4+4, P=18ft.
A=5*4, A=20ft.₂
PERIMETER AND AREA
Triangle:
P= 2x+3x+5+10 A=1/2(3x+5)(2x)
= 5x+15
=3x₂+5x
2nd round of examples:
Square:
Rectangle: 3cm.
P=6(4) P=24
5cm.
A= 6₂ A= 36
P=3+3+5+5 P= 16cm.
A=3*5 A=15cm. ₂
Triangle: P=4x+5x+3+9 A=1/2(5x+9)(4x)
= 9x+12
=5x₂+5x
CIRCUMFERENCE OF A CIRCLE
The circumference of a circle is the distance around
the circle. Circumference (C) is given by C=(Pi)d or
C=2(Pi)r.
C=2(Pi)r
C=2(Pi)r
=2(Pi)(3)=6(Pi)
=2(Pi)(11)
≈ 18.8cm
=22(Pi)
≈69.1cm.

3cm.
11cm.
AREA OF A CIRCLE
A = (Pi)r₂
 A= (Pi)r₂
= (Pi)(3)₂ = 9(Pi)
≈ 28.3cm₂
 A= (Pi)r₂
= (Pi)(11)₂
= 121(Pi)
≈380.1cm₂

3cm.
11cm.
FIVE STEP PROBLEM SOLVING PROCESS

1.READ IT CAREFULLY
2.WRITE DOWN ALL IMPORTANT INFORMATION
3.DRAW A PICTURE
4.WRITE AND SOLVE THE EQUATION
5.ANSWER THE QUESTION
FIVE STEP PROBLEM SOLVING PROCESS
1. Read it Carefully:
The quilt pattern includes 32 small triangles. Each has a base of
3 inches and a height of 1.5 in. Find the amount of fabric used
to make the 32 triangles.
2. Write down all important information:
3 inches, 32 small triangles, 1.5 inches
3. Draw a Picture
h:1.5in.

b:
FIVE STEP PROBLEM SOLVING PROCESS
4. Write and Solve the equation
b: 3in. h:1.5in. bh/2 (3)(1.5)/2 *32 = 72
5. Answer the Question
Answer: The amount of fabric used to make the 32 triangles in
the quilt is 72in₂
INTRODUCTION TO TRANSFORMATIONS

Things to know before entering transformations
Pre-image:
Image:
A
ABC
A’B’C’
TRANSFORMATIONS


A Transformation is a change in the position of the
original object.
Translation : The slide of an object in any direction
(usually is the most common) (X,Y)
(X+a,Y+b)
TRANSFORMATIONS

Rotation: to rotate a figure around a point.
TRANSFORMATIONS

Reflection: When you mirror your Pre-image across any
line. If across Y-axis (X,Y)(-X,Y). If across X-axis (X,Y)(X,Y)
JOURNAL HAS BEEN CONCLUDED

This geometry chapter 1 journal has ended,
good luck on the quiz and I hope to have
covered the topics In a satisfactory matter.