2. Point: a dot or mark that indicates a specific space. It is described as a dot with a capital letter. .P Line: a collection of straight points that form a straight edge that goes both sides forever. Plane: a flat surface that extends forever. .A .B .C
3. How to compare and contrast collinear with coplanar points: Collinear: Points that lie on the same line. ex) K, L, M are collinear; K, L, N are non collinear. <-.K--------.L--.M--> .N Coplanar: Points that lie on the same plane. ex) M and N are coplanar. L isn't. .M .N .L He difference between these two is that collinear points lie on the same line while coplanar points lie on the same plane.
4. Segment: A straight collection of points that have a beginning and an end. (A piece of a line.) ex) Ray: A straight collection of points that have a beginning but no end. ex) The difference between a line, a segment, and a ray is that a line doesn't begin OR end, a ray has a beginning but no end, and a segment has a beginning and an end.
6. Postulate: Something that needs proof and that is assumed true. Axiom: Something that is assumed true for the sake of studying it. Theorem: Something believed true to form other formulas. The difference between these three is that Postulate is just assumed true, while the axiom is believed true to study it, and the theorem is believed true based on other formulas.
7. Ruler Postulate: The distance between two points in a line. To find it, you need to use a ruler to subtract the values at each end point. Ex1) A runner has to run a 100 yard sprint. It he is currently on the 60th yard, what is the distance? 40 yards. Ex2) The Johnson family is making a 78 km trip. If they stop for gas at the 37th km, how much is the distance left for the trip to end? 41 km. Ex3) The sidewalk is 60 meters long. If I have already walked 30 meters, how much is left? 30 meters.
8. Segment Addition Postulate: If M is between L and N, then LM+MN=LN Ex1) ABC: AB=14 BC=6 14+6=20 AC=20! Ex2) HIJ: HI=45 IJ=52 45+52=97 HJ=97! Ex3)DEF: DE=12 EF=8 12+8=20 DF=20!
9. To find two points in a coordinate plane you have to use this formula: Ex1) AB= √(5-1)^2+(3-1)^2 √4^2+2^2 √16+4 √20 Ex2) DC= √(3-2)^2+(7-3)^2 √1^2+4^2 √1+16 √17 Ex3) EF= √(9-3)^2+(5-2)^2 √6^2+3^2 √36+9 √45
10. Congruent and Equality: Congruent means that it has the same measure (≈). Equality means it has the same value (=). They are similar because both compare things, while different because one has the same measure while the other same value.
11. Pythagorean Theorem: The length of the legs is equal as the sum of the hypotenuse. To find it, use this formula: a₂+b₂=c₂ Ex1) a=5 , b=6 c₂=a^2+b^2 =5^2+6^2 =25+36 =61 C=√61 Ex2) a=2 , b=3 c₂=a^2+b^2 =2^2+3^2 =4+9 =13 C=√13 Ex3) a=4 , b=6 c₂=a^2+b^2 =4^2+6^2 =16+36 =52 C=√52
12. Angles: Angles are actually two angles sharing an end point. There are three types of angles: acute (smaller than 90°), obtuse (bigger than 90°), right angle (90°), and straight angles (180°). The exterior of the angle is the “outside” part and the interior is the “inside” part. inside outside
13. Angle addition postulate: 2 angles add up to a bigger one. Ex1) ABC=34 BCD=46 34+46=80 Ex2) WXY=87 XYZ=33 87+33=120 Ex3) LMN=20 MNO=62 20+62=82
14. Midpoint (construction and formula): Midpoint is the center of a segment. To construct a midpoint first create a segment, then draw a line in the middle and draw to curves from both endpoints in the sides of the segment using a compass. Then draw a straight line in where the lines cross. The midpoint formula is (x1+x2/2, Y2+Y2/2).
15. Angle bisector (construction): The angle bisector is a way to find the exact idle of an angle. First, using your compass, make two arcs in the angle using the same measure. Then make two other arcs inside the angle and where the line intersects, well, you found the middle.
16. Adjacent: Two angles that share a vertex and a side. Linear Pair (angles): Two angles that form straight lines. Vertical: Non adjacent angles that intersect. The angles are always are congruent. Adjacent: Linear Pair: Vertical:
17. Complementary: 2 angles that add up to 90°. They are always adjacent. Supplementary: 2 angles that add up to 180°. They are always linear pairs.
18. Perimeter and Area: Square: to find the perimeter you have to add up all the sides (P=4x). To find area, square one side (A=x^2). Rectangle: to find the perimeter, add the 2 length and the 2 widths (P=2L+2W).To find area, multiply length times width. Triangle: to find the perimeter, add the three sides (P=a+b+c). for area, (bh/2).
19. Perimeter and Area examples: Square: Rectangle: Triangle: A= 10^2 =100 ft. P=10+10+10+10 =40 ft. A= 2^2 =4 ft. P=2+2+2+2 =8 ft. 10 ft. 2 ft. 10 ft. 3 ft. A=10x5 =50 ft. P=10(2)+5(2) =30 ft. A=6x3 =18ft. P=6(2)+3(2) =18 ft. 5 ft. 6 ft. A=10x3 =30/2 =15 ft. P=3+10 =13ft. A=5x4 =20/2 =10 ft. P=5+4 =ft. H=3ft. H=4ft. B=10ft. B=5ft.
20. Circumference of a circle: Circumference is the area outside the circle. To find it, use this formula: C=2(Pi)r. R=5 R=6 C=2(pi)x5 =31.4 C=2(pi)x6 =27.68
25. Answer the question!Ex) Read: Mr. Johnson wants to find the area of a certain square. He measured one side and found out it was 2 meters long. What´s the square´s area. Important info.: one side of the square equals 2m. Picture: Solve: A=2^2 =4 Answer: 4 meters. 4 meters
26. Transformations: Transformation is the change of an object from its original form. It can be changed using translation, rotation, and reflection.
