By: Harshal Nallapareddy and Eric Wang Study Guide for Quiz 1A By: Harshal Nallapareddy and Eric Wang

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Chapters Slide 4: Symmetry Slide 5: Line Symmetry Slide 6: Point Symmetry Slide 7: Transformations Slide 8: Translations Slide 9: Reflections Slide 10: Rotations Slide 11: Dilations Slide 12: Points, Lines, and Planes Slide 13: Midpoints Slide 14: PLP Vocab Page 1 Slide 15: PLP Vocab Page 2 Slide 16: Segment & Ray Vocab Page 1 Slide 17: Segment & Ray Vocab Page 2

Symmetry - Divide and Conquer The quality of being made up of exactly identical parts facing each other or around an axis. Symmetry can be used for things like knowing if a shape can be split in half, fourth, etc… There are 2 parts of Symmetry: Line and Point, Line Symmetry is when you are make a LINE of symmetry over an object and 2 or more parts are exactly identical. Point Symmetry is when there a point in the “middle” of an object and when you spin the object around a point you get the same shape at different spinning intervals.

Line Symmetry Line Symmetry is when you can slash a line across a shape and make exactly similar parts on the sides of the line. This line is called the “Line of Symmetry”. I’m sure you have heard of this term before in Elementary School. This could be used for squares, rectangles, some triangles, and even arrows. The number of Lines of Symmetry on an object, the more times it can be cut up evenly.

Point Symmetry Point Symmetry is when a shape is spun around a fixed point and is stopped whenever it looks like the original one. Like a pentagon with a dot in the middle and being spun. This can also be done to object in nature like a flower.

Transformations This is where you take a object on a coordinate plane, and move it around by Translating, reflecting, rotating, dilating.

Translation - Slidin’ around This is when you take a object and/or its coordinates, and using the verbal or algebraic method given, move them around. Verbal is when it actually tells you like saying 2 to the right or 5 up. Algebraic is when it tell you ‘x + 7’ or ‘y - 8’.

Reflection- “Mirror Mirror on the wall” This is when you take an object and/or its coordinates and reflect them over the x or y axis. Sign Rules: When you flip over the x-axis, you have to keep the x and change the sign of the y. When you flip over the y -axis, you have to change the x and keep the sign of the y.

Rotation - Upside-down, Rightside Up. This is when you take an object and/or its coordinates, and for each 90° degree turn, you have to flip the values for the x and y coordinates. The signs will depend on the quadrants. Quadrant 1 (Top right): (+ , +) (Positive, Positive) Quadrant 2 (Top left): ( - , +) (Negative, Positive) Quadrant 3 (Bottom left): (- , -) (Negative, Negative) Quadrant 4 (Bottom Right): ( + , - ) (Positive, Negative)

Dilation - The BIG Idea This is where you have to multiply by a scale factor ( 2, 3, ½ etc..). You have to multiply every number in an ordered pair. So, (2,3) will become (4, 6) if you are multiplying by a scale factor. There is one rule you have to remember, when you are going to Dilate something, you have to remember to state the enlarged ordered pairs as Primes. REMEMBER PRIMES, IT IS VERY EASY TO FORGET. YOU LIFE DEPENDS ON IT.

Points, Lines, and Planes These are the basics to Geometry, without these you are pretty much lost in the Forest of Dumbness. You have to know that points are pretty much named dots, and lines and a series of infinite dots, and planes are anything that can be stretched in more than 2 directions like a triangle, but not a line. You can also find planes on cubes and other stuff, by connecting points you can find a whole ton of them. Even though they are basic, they are still important.

Midpoint Midpoint tell you the exact middle for an object like a line segment or between 2 point on a number line. Number line formula = a + b / 2 Coordinate plane formula = (x1 + x2 / 2 , y1 + y2 / 2). This will be in ordered pair form.

Vocabulary for points, lines, planes #1 Points are made with dots. Their size is irrelevant and can vary. You label them with capital letter Lines go on forever. You can identify a line by looking at both arrows on opposite ends. You can name it with a lowercase cursive letter or put something like , but do not use 3 letters in one line. Collinear Points are points existing on the same line, visible or not. To check if a point is collinear, have it’s coords plugged in with the line’s equation. If you get something along the lines of 0=0 it’s collinear.

Vocabulary for points, lines, planes #2 Planes are 4 sided flat surfaces that can go infinitely. Usually you name them with a script letter of your choice. Remember the thing where Mrs. Petrie showed us the box? Remember that the sides can ALSO go vertically and that they don’t always have 3 points! Coplanar objects are objects that are on the same plane, visible or not Intersection of figures is the area where two figures go across each other. They can be intersecting if it is parallel to a plane, lines on it, or goes right through it. Intersection of two planes is a line. You can see it if you match up the sides that touch each other.

Segments and Rays Vocabulary #1 Postulates are anything obvious that doesn't need explaining Ruler Postulates are points on a line that can be paired with real numbers. Between is literally tell you that something is between something, whether it's an angle, plane, or line. Segments are a part of a line that have endpoints and points inside of the two endpoints. You name them with a solid line over the two line points. Segment Addition Postulates can be used like this: If C Is between A & B, Find AC + CB = AB.

Segments and Rays Vocabulary #2 Congruent segments are segments with equal lengths ⩭ is its symbol. Midpoint is a point that divides a segment into 2 congruent segments. Number Line Midpoint Formula: a + b / 2 Coordinate Plane Midpoint Formula: (x1 + x2 / 2, y1 + y2 / 2) Bisection is when a segment, line, or plane is clut with another part. The bisected line is marked with single hatch marks. Rays are lines that go infinitely one direction and stop another. Name them with an arrow over the 2 letters Opposite rays are 2 different rays who share the same endpoint. It looks like a line but the two rays are connected.

THE END We hope you have had a useful waste of your time here. We also wish you luck on the Quiz! Made by: Harshal Nallapareddy & Eric Wang.