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# Geomettry

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### Geomettry

1. 1. Guideline ____(0-10 pts.) Describe what a point, line and plane are. Give an example of each.   ____(0-10 pts.) Compare and contrast collinear points with coplanar points. Give an example and a counterexample of each.   ____(0-10 pts.) Explain what a line, segment, and ray are, and explain how they are related to each other. Give an example of each.   ____(0-10 pts.) Describe what an intersection is. Give at least 3 examples.  ____(0-10 pts.) Explain the difference between a postulate, axiom and theorem.   ____(0-10 pts.) Describe the Ruler Postulate. Give at least 3 examples.   ____(0-10 pts.) Describe the Segment Addition Postulate. Give at least 3 examples.  ____(0-10 pts.) Describe how to find the distance between two points on a coordinate plane. Give at least 3 examples.  ____(0-10 pts.) Describe what congruence is and compare it to equality. Give an example of how they are different. Give an example of how they are similar.  ____(0-10 pts.) Describe the Pythagorean Theorem. Give at least 3 examples.  ____(0-10 pts.) Describe what an angle is and how they are measured. Be sure to include a discussion about the parts of an angle, and the different types of angles. Give an example of each.  ____(0-10 pts.) Describe the Angle Addition Postulate. Give at least 3 examples. ____(0-10 pts.) Describe what a midpoint is and how it can be constructed, and how it can be found using the midpoint formula. Give at least 3 examples. ____(0-10 pts.) Describe what an angle bisector is, and how to construct one. Give an example.   ____(0-10 pts.) Describe what adjacent, vertical and linear pairs of angles are. Give an example of each. ____(0-10 pts.) Compare and contrast complementary and supplementary angles. Give examples of each.   ____(0-10 pts.) Describe how to find the perimeter and area for the following shapes: square, rectangle and triangle. Give 2 examples of each.   ____(0-10 pts.) Describe how to find the area and circumference of a circle. Give 2 examples.   ____(0-10 pts.) Describe the five-step process for solving any problem you encounter this year. Give an example, clearly showing all five steps.   ____(0-10pts.) Describe what a transformation is and how they change the original object. Give at least 3 examples.   ____(0-5 pts.) Neatness and originality bonus   _____Total points earned (200 possible)
2. 2. Geometry Journal # 1 Point, Line and Plane Collinear and Copplanar points Ray,line and segment relathionship Questions 1-3 Next 4 problems
3. 3. Point, Line and Planes Whats a Point ? Whats a line ? Whats a plane The name for a location represented with a dot. It has no specific size you write it as a capital letter in this case A,B Examples here A and B are both points B A A line is a straight path that has no thickness and extends forever unles stoped by an endpoint. You write it as a lower case letter or two points on a line example e or <-------> XY Example of a line A plane is a flat surface that has ni thickness and extends forever. Here is where your points and lines go. You write it as a script capital letter or 3 points together R or ABC C
4. 4. Collinear and Coplanar points Collinear points are the points located inside a line,ray or segment. Copplanar points are the points located inside the plane but they are like free points which are not part of a line. Both are similar because the are inside a plane and they are points or coordenates. But they are different because one from a line and the other one is free inside the plane B A A and C are collinear and B,A,C coplanar C
5. 5. Ray,line and segment relathionship Ray Segment Line How do they relate? A line with one standing point and then extending forever into that direction You write it as ----  RS A segment,fraction,part of a line. It consits of 2 points between the line. You write it as ------- MN R S M N A line is a straight path that has no thickness and extends forever unles stoped by an endpoint. You write it as a lower case letter or two points on a line example e or <-------> XY They all relate because all have points and are parts of a line. Segments and Rays have endpoints. Segments are parts of lines and Rays go towards an nonstoping line.
6. 6. Questions 4-8 Intersections Postulate,Axiom and Theorem Ruler postulate Segment addition postulate
7. 7. Intersections An intersection is the set of all points that two or more lines have in common. Its the point where lines cross and it marks a difference because it the only time where this two lines can join. Examples Inter state 44 and Inter state 45 join at Km 44 Carretera a el Salvador The Greenwhich line intersect the tropic of capricorn 44 45 Line A Intersects with line B A B
8. 8. Postulate,Axiom and Theorem Postulate or Axiom: Any rule we don't have to prove it's a fact Theorem: A statement that has been proven They are all similar because they are proven (facts) they state reality and explain. They dont need to be proven because the answer to them is always the same 2+2=4 always……
9. 9. Ruler postulate To measure a segment you use a ruler and substract the values of the end points. Ruler 1 2
10. 10. Segment addition postulate If 3 collinear points with B inbetween A and C then AB+BC=AC Examples 1.) 2.) 3.) 1 5 9 A B C AB=4 BC=4 so AC=8 10 12 18 AB=2 BC=6 so AC=8 1 10 11 AB=9 BC=1 AC=10
11. 11. <ul><li>Describe what congruence is and compare it to equality. Give an example of how they are different. Give an example of how they are similar  </li></ul><ul><li>Describe the Pythagorean Theorem. Give at least 3 examples. </li></ul><ul><li>Describe what an angle is and how they are measured. Be sure to include a discussion about the parts of an angle, and the different types of angles. Give an example of each </li></ul><ul><li>____(0-10 pts.) Describe the Angle Addition Postulate. Give at least 3 examples. </li></ul>Journal problems 9-12
12. 12. Describe what congruence is and compare it to equality. Give an example of how they are different. Give an example of how they are similar <ul><li>Congruent: they are the same measure. Might not know what each value is worth. </li></ul><ul><li>Equal: Same value. You have to know the values </li></ul><ul><li>Different A---------------B is congruent to </li></ul><ul><li>D---------------C and you couldt say they where equal to each other if A=2,B=3 and D=1,C=4 </li></ul><ul><li>Similar: </li></ul><ul><li>AB=5 and CD=5 </li></ul>
13. 13. Pythagoream Theorem <ul><li>a2+b2=c2 It is used to find the hypotenuse of a right triangle. When re arranged we can also find the other sides. </li></ul>4 4 4 4 2+3 2 =c2 16+9 =c2 25 =c2 5 = c 3 5 7 2 + 7 2 =c2 49 + 49 =c2 98 = c2 C = 9.898 2 5 2 2 plus 5 2=c2 4 plus 25= 29 29 = c2 C = 5.39
14. 14. Describe what an angle is and how they are measured. Be sure to include a discussion about the parts of an angle, and the different types of angles. Give an example of each <ul><li>A shape formed when two rays that share a common end point are put together. Angles are meassured by degrees. There are different types of angles. </li></ul><ul><li>Obtuse angle bigger than 90*degrees </li></ul><ul><li>Acute angle less than 90* degrees </li></ul><ul><li>Right angle 90*degrees </li></ul><ul><li>Straight angle 180*degrees </li></ul><ul><li>Adjacent angle:Two angles that share a common side </li></ul><ul><li>Linear pair: Two angles that share a common side and form a straight line </li></ul><ul><li>Complementary L’s: Two angles that add up to 90* degrees </li></ul><ul><li>Supplementary L’s: any two angles that add up to 180*degrees </li></ul>
15. 15. Describe the Angle Addition Postulate. Give at least 3 examples. <ul><li>This postulate is similar to the segment addition postulate but in here we add the angles instead of adding the segments , </li></ul><ul><li>Examples </li></ul>45 45 5 85 90 30 45 plus 45 =90’degrees 85 plus 5 = 90’ degrees 90 plus 30=120’ degrees
16. 16. <ul><li>Describe what a midpoint is and how it can be constructed, and how it can be found using the midpoint formula. Give at least 3 examples. </li></ul><ul><li>Describe what an angle bisector is, and how to construct one. Give an example </li></ul><ul><li>Describe what adjacent, vertical and linear pairs of angles are. Give an example of each. </li></ul><ul><li>Compare and contrast complementary and supplementary angles. Give examples of each. </li></ul>Geometry 13-16
17. 17. Describe what a midpoint is and how it can be constructed, and how it can be found using the midpoint formula. Give at least 3 examples.
18. 18. Describe what an angle bisector is, and how to construct one. Give an example <ul><li>Angle Bisector: The angle bisector is the ray in the middle of an angle which makes one angle into two congruent angle. Bisecting the angle. We do this with a compass at the endpoint then we establish an intersecting arc which we Awe draw a line which will finnaly be our bisector </li></ul>
19. 19. Describe what adjacent, vertical and linear pairs of angles are. Give an example of each. <ul><li>Vertical: Non adjacent C’s formed by the intersection of 2 lines </li></ul><ul><li>Linear pair: Two angles that share a common side and form a straight line </li></ul><ul><li>Adjacent angle:Two angles that share a common side </li></ul>
20. 20. Compare and contrast complementary and supplementary angles. Give examples of each. <ul><li>Well a complementary is two angle that together add up to 90* degrees. Then we have the supplementary angles which add up to 180*degrees. They are similar because both add up to form a specific degree. But whats different is that complementary angles share a common end point where as supplementary angles dont. </li></ul>Complementary Supplementary
21. 21. Describe how to find the distance between two points on a coordinate plane. Give at least 3 examples.
22. 22. More…. <ul><li>Describe how to find the perimeter and area for the following shapes: square, rectangle and triangle. Give 2 examples of each. </li></ul><ul><li>  </li></ul><ul><li>Describe how to find the area and circumference of a circle. Give 2 examples. </li></ul><ul><li>  </li></ul><ul><li>Describe the five-step process for solving any problem you encounter this year. Give an example, clearly showing all five steps. </li></ul><ul><li>Describe what a transformation is and how they change the original object. Give at least 3 examples. </li></ul>
23. 23. Describe how to find the perimeter and area for the following shapes: square, rectangle and triangle. Give 2 examples of each. <ul><li>Rectangle: to find the perimeter you use the following formula </li></ul><ul><li>2 lenght + 2 widht and to find the are you use lenght times width or lw </li></ul><ul><li>Square: to find the perimeter you multiply the side times 4 and you square the side to get the area. </li></ul><ul><li>Triangle: to find the perimeter you add a+b+c and to find the area you multiply the base times the height and divide it by 2. </li></ul>Example 4 6 3 2 5 4 2 Area 2 x 4/2 =4 Perimeter 2+2+5 =9 Perimeter 3 x 4 =12 Area 3 2=9 Perimeter 4x4 +6x6= 52 Area 6 x 4=24
24. 24. More examples on are and perimeter 5 3 5 5 10 10 5 Area 5x102 = 25 Perimeter 10 +10 +5=25 Area 5 2=25 Perimeter 5X4 =20 Area 5x3=15 Perimeter 3x2+5x2=16
25. 25. Describe how to find the area and circumference of a circle. Give 2 examples. <ul><li>Circunference and area of a circle. Well first of all these two formulas are basic and easy ones which’s goal is to find the measurements around and inside the circle. </li></ul><ul><li>Formulas </li></ul><ul><li>Circumference: C = 2pi (3.14) r </li></ul><ul><li>Area = pi(3.14)r 2 </li></ul><ul><li>Examples </li></ul>5 3 C = 2pi3 6pi =18.84 A=3.14x3 2 =9xpi =28.26 C= 2pi5 10xpi= 31.4 A= 3.14x5 2 25x3.14=78.5
26. 26. Describe the five-step process for solving any problem you encounter this year. Give an example, clearly showing all five steps
27. 27. Describe what a transformation is and how they change the original object. Give at least 3 examples. <ul><li>Transfomation: the change of a figure </li></ul><ul><li>Types: </li></ul><ul><li>Translation: to slide the shape conseving the shape and size. Basically moving the image from place to place </li></ul><ul><li>Reflection: to flip the image across any line as if it where a mirror. </li></ul><ul><li>Rotation: to spin an image around its point. </li></ul><ul><li>Examples </li></ul>