1. Gabriela Gottlib Geometry Journal #1

2. 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

3. 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.

4. 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.

5. Intersection: When two lines cross each other. Example 1: Example 2: Example 3: Real life Example: Street

6. 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.

7. 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. 418 18-4=14 222 22-2=20 8 15 15-8=7

8. 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

9. 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

10. 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

11. The Pythagorean theorem is that: a 2 + b 2 = c 2 1. 5 12 c 5 2 +12 2= C 2 25+144= c 2 169=c 2 C=√169C=13 a b c a b c

12. 2. 3. 8 3 c 8 2 +3 2= C 2 16+9= c 2 25=c 2 C=√25 C=5 9 2 +12 2= C 2 81+144= c 2 225=c 2 C=√225 C=15 9 12 c

13. The angle addition postulate says that two small angles ass up to the big angle. 90 35 125 90 45 25 50 90+35=12545+45=9025+25=50

14. 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) 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

15. 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 >

16. 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

17. 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

18. 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 °

19. 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

20. 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: 12+12+10= 34cm A: ½(8*10)= 40cm 8cm 10 cm P: 10+10+8= 28cm A: ½(5*8)= 20cm 5cm

21. Area: Pi*r 2 Circumference: Pi*d or 2*Pi*r 1. 2. 3 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

22. 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

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

24. 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

25. 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’

26. When you twist a shape around any point. A CB A’ C’B’

27. 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