Points, Lines, and Planes Point: it is a mark or a dot that marks the location of something. Line: a collection of straight points that form a straight edge. Planes: it is a flat surface which extends forever.
Collinear Points and Coplanar Points C A Collinear points are the ones that lie on the same line. B G E A B C F H D P M O G Coplanar points are the ones that lie on the same plane. R S
Line, Segments and Rays Line: a line is a collection of straight points that form a straight edge B Segments: part of a line consisting of two points and all in-between. A AB Rays: part of line that starts at one end point and extends forever in one direction. They all relate to each other since they are all straight edges or linesand they all use points.
Intersection An Intersection is where two lines meet in a specific pointin any situation.
Postulate, Axiom, and Theorem Postulate and Axiom are the same thing. They are terms that are accepted without proofs. While a Theorem has to be accepted only if there if proof and it has already been proven.
Ruler Postulate To measure a segment you need to use a ruler and subtract the values at the end points. The hallway is 60 meters and a student runs from 25 meter up to the end, how many meters did he run? 35meters If my garden if 148 meter long, and my cousin started rolling from 40 meters and he reaches the wall, how many meters has he rolled? 108meters Rodrigo’s desk is 4 meters and he makes a car travel from one end to the other, how many meters has he traveled? 4meters
Segment Addition Postulate C For example, if we have “B”, “G” and “H” but “G” is between “H” and “B”, then “BG” and “GH” = “BH” 15 B 30 45 B A H J 6 6 K Q 12 G
Distance Between Two Points on a Coordinate Plane If you want to find the distance between two points on a coordinate plane you just need to take “X”1 and “X”2 and square them. Do the same for “Y”1 and “Y”2. After that you add those two and square the final answer.
Congruence and Equality Congruence is two things with the same measure, but might not know the value. It is similar to equality since they are both two things that are equal. They are different because you can see if both shapes are congruent but if you don’t have a value you cannot see if they are equal, so with congruence you just need a measure but with equality you need a value.
Pythagorean Theorem The Pythagorean theorem is when in a right triangle, the sum of the squares of the length(legs) is equal to the square of the length(hypotenuse) a²+b²=c² a=6 and b=4 a=2 and b=3 a=9 and b=9 6²=36 2²=4 9²=81 4²=16 3²=9 9²=81 So, c=52 So, c=13 So, c=162 52² 13² 162 ² 2,704 169 26,244
Angles An angle is: two rays that share a common end point and they are measured with a protractor. The different types of angles are: right, obtuse and acute. The right angles are the ones that measure 90ᵒ. The obtuse angles are the ones that measure more than 90ᵒ. The acute angles are the ones that measure less than 90ᵒ. Acute Obtuse Right
Angle Addition Postulate The Angle Addition Postulate is two angles adding up to a bigger angle. ABD=50 ABC=180 180-50=30 DBC=30 FJH=170 HJI=40 170-40=30 FJI=30 D C A B
Midpoint A midpoint is the exact middle of a segment. It is like if it is cut in the perfect half. To find the midpoint you need to get a little passed the middle, with your compass you draw a line from one side, and then do the same for the other. When done, you need to draw a line between the two lines you drew which formed an “X” and there you have your midpoint!
Angle Bisector An Angle Bisector is when you cut now the angle in half. Place the compass in any measurement you want. Draw an arc on each line of the angle placing the compass in the vertex of the angle. Then, make an arc placing you compass right in the intersection of the arc and line of the sides, to wherever the compass reaches(remember, don’t change the measurement!)
Adjacent, Vertical and Linear Pairs Adjacent Angles are two angles that have the same vertex and share a side. Linear Pair are two adjacent angles that form a line. Vertical Angles are non-adjacent angles formed when two lines intersect. They are ALWAYS congruent. Linear Pair Adjacent Vertical
Complementary and Supplementary Angles Complementary Angles are any two angles that add up to 90ᵒ and Supplementary Angles(example of linear pair) are any two that add up to 180ᵒ . Supplementary Angle Complementary Angle
Area And Circumference of a Circle A= (Pi)r² C=2(Pi)r
Five Step Process First you need to read the problem patiently, don’t give up on the first time you read it. Read it a couple of times if needed. Then, jot down the key words that we learned in the beginning of the year and other words that are important. Write a problem with all those key words, translations and etc. Then solve the problem and check your answer to see if it is correct. Last but not least, answer the question in a complete sentence or with the units.