Gabriela Gottlib Geometry Journal #1

Point: A point is a dot that describes a location When 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 directions A 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 forever A plane has a letter that means what is the name for it. A PGB A B G H SMO

Collinear Points: Collinear points are points that are in the same line. Coplanar Points: Coplanar points are points that are in the same plane. A B A B A B C They are the same because they both involve points and where they are located.

Line: A point is a dot that describes a location When 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. A B G H 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

Postulate: A postulate is a statement that is accepted true without proof. (Axiom) Axiom Axiom is also a statement that is accepted true without proof. (Postulate) Theorem A theorem is a statement that has been proved. 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 = = =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: 5BC:3AC:8 AB C AB C AB: 5BC:10AC:15 AB: 3BC:3AC:6 ABC

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: a 2 + b 2 = c c = C = c 2 169=c 2 C=√169C=13 a b c a b c

c = C = c 2 25=c 2 C=√25 C= = C = c 2 225=c 2 C=√225 C= c

The angle addition postulate says that two small angles ass up to the big angle = = =50

Midpoint: Center of a segment Steps: 1 st : Open the compass half way through the line 2 nd : put it in one side and do an arch up and down of the line 3 rd : Put it in the other side and do the same thing 4 th : You connect the middle of the two arches Midpoint with formula: (x1+x2, y1+y2) 22 1.(–1, 2) and (3, –6). (-1+3, 2+-6) = (1,-2) (5, 2) and (5, –14). (5+5, 2+-14) = (5,-6) (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 ExteriorExterior If an angle is named: BAC then the vertex is A because you always write the vertex in the middle Right angle 90 Acute angle 90 < Obtuse angle 90 >

To bisect something is to cut it in half. So to bisect an angle is to divide the angle in half. Steps: 1 st : Put the compass in the vertex of the angle 2 nd : Draw an arch on both sides of the angle 3 rd : Put the compass in the arch and draw another arch up 4 th : 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 Common Side

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 °

Perimeter: The sides of a shape Area: The space inside of a shape Square P: 4s A: s2 Rectangle P: 2l + 2w A: lw Triangle P: a+b+c A: ½bh

Example 1:Example 2: 8cm P: 4(8)= 32 cm A: 8’2= 64 cm 10cm P: 4(10)= 40 cm A: 10’2= 100 cm 10 cm 5 cm P: 2(10)+2(5)= 30cm A: 10(5)= 50 cm 8 cm 2 cm P: 2(8)+2(2)= 20cm A: 8(2)= 16cm 10 cm 12 cm P: = 34cm A: ½(8*10)= 40cm 8cm 10 cm P: = 28cm A: ½(5*8)= 20cm 5cm

Area: Pi*r 2 Circumference: Pi*d or 2*Pi*r in Area:3.14*3 2 = 28.26in Circumference:3.14*6= 18.84in 5 in Area:3.14*5 2 = 78.5in Circumference:3.14*10= 31.4in

Steps: 1.Read the problem 2.Rewrite any important information 3.Create a visual with the information given 4.Solve the equation 5.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= RS=1635 RY=817.5 XY= XR+RY = = m 5.You are 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’G’H’I’ There are three types of transformations: o Translation o Rotation o 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 CB 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 X Y=X