Gabriela Gottlib

Geometry Journal #1

Point: A point is a dot that describes a locationWhen you are given a point it always has a capital letter for it. That is its name.

Line: A line is a straight collection of dots that go on forever in both directionsA line always is named by the two letters it has on any part of it

Plane: A plane is a flat surface that extends on foreverA plane has a letter that means what is the name for it.

A P G B

AB

GH

S MO

AB

A B

A

BC

They are the same because they both involve points and where they are located.

Line: A point is a dot that describes a locationWhen you are given a point it always has a capital letter for it. That is its name.

Segment: A line that has a beginning and end

(Part of a line)

Ray: A line that in one side keeps on forever and in the other side stops.

AB

GH

They are related to one another because they have to be straight. Also because they are lines.

Intersection: When two lines cross each other.

Example 1:

Example 2:

Example 3:

Real life Example:Street

The difference between those three is that a postulate and axiom DON’T need a statement to proof it true and a for a theorem you DO need a statement to accept it as true.

The ruler postulate says that when you measure any segment you use a ruler and you don’t always have to start at 0. You can just subtract both end points and that way you can know the measure of the segment also.

4 18

18-4=14

2 22

22-2=20

8 15

15-8=7

The segment addition postulate says that if A,B and C are 3 collinear points and B is between A and C, then AB and BC= AC

In other words it is telling that the measurement of AB and the measurement of BC will always equal the measurement of AC

AB: 5 BC:3 AC:8

A B C

A B C

AB: 5 BC:10 AC:15

AB: 3 BC:3 AC:6

A B C

Distance= √(x2-x1) 2 + (y2-y1) 2 Example 1: (1,-2) (3,-4)D=√(1-3) 2 +(-2- -4) 2

√4+36= √40√40

Example 2: (2,-3) (4,-5)D=√(2-4) 2 +(-3- -5) 2

√4+64= √68√68

Example 3: (3,-4) (5,-6)D=√(3-5) 2 +(-4- -6) 2

√4+100= √104√104

Congruent• You use congruent

when you have two things with equal measures.

• You might not know the value

AB = CD

Equal• You use equal when

two things have an the same value

• We have to know the value in order to use the word

AB=3.2

They are similar because they are both used to compare

The Pythagorean theorem is that: a2 + b2 = c2

1.

5

12

c

52+122=C2

25+144= c2

169=c2 C=√169C=13

ab

cab

c

2.

3.

8

3

c

82+32=C2

16+9= c2

25=c2 C=√25C=5

92+122=C2

81+144= c2

225=c2 C=√225 C=159

12

c

The angle addition postulate says that two small angles ass up to the big angle.

90

35

125

90

45

45

25

25

50

90+35=125 45+45=90 25+25=50

Midpoint: Center of a segmentSteps: 1st: Open the compass half way through the line2nd: put it in one side and do an arch up and down of the line3rd: Put it in the other side and do the same thing4th: You connect the middle of the two arches

Midpoint with formula:(x1+x2 , y1+y2) 2 2

1. (–1, 2) and (3, –6).(-1+3 , 2+-6) = (1,-2) 2 2

2. (5, 2) and (5, –14).(5+5 , 2+-14) = (5,-6) 2 2

3. (7, 2) and (5, –6).(7+5 , 2+-6) = (6,-2) 2 2

Angles are two rays that share the same end point.They are measured by using a protractor. There are three types of angles: Acute, Obtuse and Right.

Vertex

Interior

Exterior

If an angle is named: BAC then the vertex is A because you always write the vertex in the middle

Right angle90

Acute angle90 <

Obtuse angle90 >

To bisect something is to cut it in half. So to bisect an angle is to divide the angle in half.

Steps:1st: Put the compass in the vertex of the angle2nd: Draw an arch on both sides of the angle3rd: Put the compass in the arch and draw another arch up4th: Do the same thing in the other side

Adjacent angles: Two angles that have the same vertex and they share a side

Vertical angles: Two non adjacent angles formed when two lines intersect

Linear pair angles: Two adjacent angles that form a straight line

Comm

on S

ide

Complementary• Complementary

angles ALLWAYS have to add up to 90°

Supplementary• Supplementary angles

ALLWAYS have to add up to 180°

They are similar because they have to do with angles and measurements. They are different because they have to add up to a different number

75°

15°90°

90°

Perimeter: The sides of a shape Area: The space inside of a shape

Example 1:Example 2:

Example 1:Example 2:

Example 1:Example 2:

8cm

P: 4(8)= 32 cmA: 8’2= 64 cm

10cm

P: 4(10)= 40 cmA: 10’2= 100 cm

10 cm

5 cm

P: 2(10)+2(5)= 30cmA: 10(5)= 50 cm

8 cm

2 cm

P: 2(8)+2(2)= 20cmA: 8(2)= 16cm

10 cm

12 cm 12 cm

P: 12+12+10= 34cm A: ½(8*10)= 40cm

8cm

8 cm

10 cm 10 cm

P: 10+10+8= 28cm A: ½(5*8)= 20cm

5cm

Area: Pi*r2 Circumference: Pi*d or 2*Pi*r

1.

2.

3 in

Area:3.14*32= 28.26inCircumference: 3.14*6= 18.84in

5 in

Area:3.14*52= 78.5in

Circumference: 3.14*10= 31.4in

Steps:1. Read the problem2. Rewrite any important information3. Create a visual with the information

given4. Solve the equation5. Answer the problem

1. You are 365m from the drink station R and 2km from drink station S. The first-aid station is located at the midpoint of the two drink stations. How far are you from the first-aid station?

2. XS= 2km XR= 365m

3. X R Y S

2 km

365m

4. XR+RS=XS 365+RS=200-365 -365RS=1635RY=817.5

XY= XR+RY

=365+817.5= 1182.5 m

5. You are 1182.5 m from the first-aid station.

X R Y S

2 km

365m

1. You are 365m from the drink station R and 2km from drink station S. The first-aid station is located at the midpoint of the two drink stations. How far are you from the first-aid station?

A transformation is when you change the position of an object.

Pre- Image: Image:GHI G’H’I’

There are three types of transformations:

o Translationo Rotationo Reflection

When you slide an object in any direction.

(x,y)(x+a, y+b)

After the pre-image you need to add ‘ (PRIME) to the image

A

CB

A’

C’B’

When you twist a shape around any point.

A

C

B

A’

C’

B’

When you mirror the pre-image across the line.

If across Y axis: (X,Y) (-X,Y) X becomes negative and Y stays the same

If across X axis: (X,Y) (X, -Y) X stays the same and Y becomes opposite

If we reflect across the line: (X,Y) (Y,X) You put X in Y and Y in XY=X