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Gabriela Gottlib

Gabriela Gottlib. Geometry Journal #1. What is a Point, Line, Plane. 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

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Gabriela Gottlib

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  1. Gabriela Gottlib Geometry Journal #1

  2. What is a Point, Line, Plane 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 P G B B A G H S O M

  3. Collinear and Coplanar Points A B A C B A B They are the same because they both involve points and where they are located.

  4. Line, Segment and Rays 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. B A G H They are related to one another because they have to be straight. Also because they are lines.

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

  6. Postulate, Axiom and Theorem: 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. Ruler Postulate: 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

  8. Segment Addition Postulate: 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 A B In other words it is telling that the measurement of AB and the measurement of BC will always equal the measurement of AC C AB: 5 BC:3 AC:8 A B C AB: 5 BC:10 AC:15 A B C AB: 3 BC:3 AC:6

  9. Distance Between Two Points In a Coordinate Plain : 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 VS. Equal: Congruent 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 • You use congruent when you have two things with equal measures. • You might not know the value AB = CD They are similar because they are both used to compare

  11. Pythagorean Theorem: The Pythagorean theorem is that: a2 + b2 = c2 52+122=C2 c c 25+144= c2 a a C=√169 C=13 169=c2 b b 1. c 5 12

  12. 2. 3. c 8 3 82+32=C2 92+122=C2 16+9= c2 81+144= c2 C=√25 C=5 C=√225 C=15 25=c2 225=c2 c 9 12

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

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

  16. Angle Bisector: 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 angle 2nd: Draw an arch on both sides of the angle 3rd: Put the compass in the arch and draw another arch up 4th: Do the same thing in the other side

  17. Adjacent, Vertical and Linear pair of angles: 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 VS. Supplementary: Complementary Supplementary Supplementary angles ALLWAYS have to add up to 180° • Complementary angles ALLWAYS have to add up to 90° 75° 90° 15° 90° 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

  19. Perimeter and Area: Perimeter: The sides of a shape Area: The space inside of a shape

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

  21. Area and Circumference of a Circle: Area: Pi*r2 Circumference: Pi*d or 2*Pi*r 1. 2. Area: 3.14*32= 28.26in Circumference: 3.14*6= 18.84in 3 in Area: 3.14*52= 78.5in Circumference: 3.14*10= 31.4in 5 in

  22. Five Steps to Solve any Problem: Steps: Read the problem Rewrite any important information Create a visual with the information given Solve the equation Answer the problem 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? XS= 2km XR= 365m 3. X Y R S 365m 2 km

  23. XR+RS=XS 365+RS=200 -365 -365 RS=1635 RY=817.5 XY= XR+RY =365+817.5= 1182.5 m You are 1182.5 m from the first-aid station. 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? X Y R S 365m 2 km

  24. Transformation: A transformation is when you change the position of an object. Pre- Image: GHI Image: G’H’I’ • There are three types of transformations: • Translation • Rotation • Reflection

  25. #1: Translation 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 A’ B C B’ C’

  26. #2: Rotation When you twist a shape around any point. A A’ B C B’ C’

  27. #3: Reflection 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

  28. The End  The End  The End  The End  The End 

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