1. Geometry Journal Michelle Habie 9-3

2. Point, Line, Plane Point: A mark or dot that indicates a location. Ex: Line: A straight collection of dots that go on forever. Ex: Plane: Flat surface that extends forever. Ex:

3. Collinear Points & Coplanar Points: Collinear Points: Points that are in the same line. Ex: Non collinear Points: Points that are not in the same line. Ex: Coplanar Points: Points that are on the same plane. Ex: This is an example of coplanar points that are not collinear. This 3 points are coplanar and collinear.

4. Line, Segment, Ray Line: A straight collection of dots that go on forever. Ex: Segment: A line that has a beginning and an end. Ex: Ray: A line that has a starting point and in one side it keeps on going forever and in the other side, it stops. Ex: The three of them join two points however, some stop and other continues their path.

5. What is an intersection? Intersection: The point where a line crosses the x axis or the y axis. Passing across each other at exactly one point. Exmples: 1.2.3. Real Life Intersection

6. Postulate, Axiom, Theorem: Difference: Postulate: A statement that is accepted as true without proof. Axiom: A statement that is accepted as true without proof. Theorem: A statement that has been proven.

7. Ruler Postulate: To measure any segment you use a ruler and subtract the values at the end points. Examples: 1. 2. 3. 5 5 8 8 B B A A Base 2 Base 1 Use the ruler postulate to find the distance from one point to the other.

8. Segment Addition Postulate: If A,B and C are 3 collinear points and B is between A and C then AB+BC=AC. Examples: A A C C B B 1 1 2 2 3 3 CAG Vista Hermo sa Blvd. Home Use this postulate to find the distant between 3 or more points on a segment.

9. Distance between 2 points: To find the distance between two points you use the distance formula: √(x2-x1) ⌃ 2+(y2-y1) ⌃ 2 Examples: 1. (2,4) (-1,0) D=√(2+1) ⌃ 2+(4-0) ⌃ 2= D=5 2. (3,-2) (6,-8) D=√(3-6) ⌃ 2+(-2+8) ⌃ 2= D=√45 3. (1,0) (-2,8) D=√(1=2) ⌃ 2+(0-8) ⌃ 2= D=√73

10. Congruent – Equal: ≅ Two things that have equal measure. Might not know what the value is. Comparing Names. -- ≅ -- AB CD = Two things that have the same value. We have to know the value Comparing Values AB=3.2 Examples : B B A A C C A, B are congruent and equal. While B, C are congruent but, not equal.

11. Pythagorean Theorem: The sum of the legs to the squared has to be equal to the hipothenuse to the square. Examples: a 2+ b 2= c 2 If a=10 and b=12 Find c: c=√(10 2 ) + (12 2 ) C=√244 Find a A=√10 ⌃ 2-8 ⌃ 2 A=√100-64 A=√36=6 A=10 c=16 Find b b=√16 ⌃ 2-10 ⌃ 2 B=√256-100 = b=√156 B=8 c=10

12. Angles and types of angles: An angle is the joining of two rays with a common point called vertex. We measure the angles by the distance from ray to ray, we measure them in degrees. 1. Acute angle (measures 0°-89°) 2. Right angle (measures exactly 90°) 3. Obtuse angle (measures between 91°-179°) 4. Straight angle (measures exactly 180°) The parts of an angle are its legs and the vertex. Legs Interior Vertex

13. Angle addition Postulate: The measurement of two included angles is equal to the measurement of the whole angle that includes both. <CAD+<CAB=<BAD1. m<CAD= 30° m<CAB=20° Find m<BAD m<BAD=30°+20°=50° 2. m<BAD= 75° and m<CAD= 15° Find m< CAB m<CAB=75°-15°=60° 3. <EIF=32°, <FIG=40°, <GIH=38° Find m<EIH m<EIH=32°+40°+38°=110° A B C D E F G H I

14. Midpoint The midpoint is the point that bisects a segment in two congruent parts. You can find a midpoint by measuring or using a straight edge( compass). Examples: 1. A C is the midpoint Because lies in the middle of segment A,C. B E F If EF= 10 and FG= 9, then F is NOT the midpoint of EG. G The apple balances this scale because it represents the midpoint.

15. Angle Bisector: It means to divide an angle into two congruent angles. To construct an angle bisector you use a compass and a ruler to find it. Example 1 :

16. Adjacent,Vertical, Linear Pairs of Angles: Adjacent: Have a common vertex sharing a ray with no common interior points. Vertical: Two non adjacent angles form by two intersecting lines. Linear: Adjacent angles with non common sides are opposite rays.

17. Supplementary & Complementary Angles: Supplementary : Any two angles that add up to 180° Complementary : Any two angles that add up to 90°

18. Area and Perimeter of Shapes: A= s ⌃ 2 P= 4s Example 1 : s=5in A=(5) ⌃ 2=25in ⌃ 2 P=4×5=20in Example 2: s=3cm A=(3) ⌃ 2=9cm ⌃ 2 P=4×3=12 cm A= l w P= 2l + 2w Example 1 : l= 2 cm, w= 1 cm A = 2×1=2cm ⌃ 2 P =2(2)+ 2(1)=6cm Example 2:l= 5 ft, w=3ft A= 5×3=15ft ⌃ 2 P= 2(5)+ 2(3)= 16ft A= ½ l h L= a+b+c Example 1 : l= 5, w= 3, b=4, c=6 A = 5×3÷2= 7.5 u ⌃ 2 L = 5+4+6= 15u Example 2:l=7, w=4, b=2, c=5 A= 7×4÷2= 14u ⌃ 2 L=7+2+5= 14u

19. Area and Circumference of a Circle Area= π r ⌃ 2 Example 1: r= 6 A(3.14)(6) ⌃ 2 A=3.14×36 A=112.04u ⌃ 2 Circumference: 2π r Example 1: r= 8cm c= 2(3.14)(8) c= 50.24cm

20. 5 Step Process: If three cans of soda cost $10.50. How much would seven cans of soda cost? 1.Read it carefully. 2.Understand the problem 3.Make a plan- I definetly need to set up a proportion. 4.3 cans=7 cans ------ = ------ = 10.50 ×7 10.50 x------------ 3 x=$24.50 5. Look Back if the answer makes sense.

21. Transformations: Make a copy of a figure in a different position. A transformation can enlarge an object or shrink an object. Examples: Rotate Reflect Translate

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