October 22, 2018

Archives for June 2013

Common Core Math 2 – Geometry Unit 1 Vocabulary

As I begin to help students at , a tutoring center in Apex, NC prepare for Common Core Math 2 / Geometry, I have decided to include some of the material online to make it available to all students who are beginning this course. The first thing that a student needs to know about Geometry is that one must learn all of the vocabulary and theorems in order to be successful. There is no other way to be successful in this class. Therefore, I will start with a list of the beginning vocabulary that one should learn and focus on as they begin to study for this course.

Line – Most students know what a line is but it is important to note that a line has arrows in both directions, note it is different from a line segment that terminates with end points.

Line Segment – A part of a line that terminates with a point at either end.

Ray – A mix between a line and a line segment, one end has a point, the other end an arrow.

Plane – Think of a desktop that continues infinitely in all directions.

Co-linear – Points that are co-linear would be points that fall on the same line.

Midpoint – This is the exact middle of a line segment, it divides something into two equal halves. The formula for calculating a midpoint doesn’t need to be memorized if you just remember that it is the average of the x-values and the average of the y-values.

Acute angle – A “cute” small angle that is greater than 0 degrees but less than 90 degrees.

Right angle – An angle that is exactly 90 degrees. We put a box in the corner of the angle to show it is right. In Geometry, we cannot assume an angle is right just by looking at it, if we don’t have proof or see the “box” we cannot assume it is 90 degrees even if it “looks” right.

Obtuse angle – An “obese” angle or fat angle, one that is greater than 90 but less than 180.

Straight angle – A angle that forms a line and measures 180 degrees.

Complementary – Two angles who sum to 90 degrees.

Supplementary – Two angles who sum to 180 degrees.

Adjacent angles – Angles that are next to each other.

Linear Pair – Two adjacent angles that are supplementary.

Bisect – Something that cuts into two equal pieces such as an angle bisector would cut the angle into two equal pieces.

Vertical Angles – Angles opposite each other (often form an X) – vertical angles are complementary.

Perpendicular Bisector – A line that bisects another line by hitting it at a right angle and cutting it into two equal pieces.

Distance between two points – Memorize distance formula or learn how to use the Pythagorean Theorem to find the distance between any two ordered pairs.

Perimeter – Distance around an object.

Circumference – The distance around a circle: C = PI X Diameter.

Area – The space inside a shape.

Radius – The distance from the center of the circle to the one end of the circle. Radius is half the diameter.

Diameter – The distance from one side of a circle to the other going through the center of the circle. Diameter is twice the radius.

Addition Property of Equality: When you add the same number to both sides of an equation, it doesn’t effect the equality of the equation.

Subtraction Property of Equality: When you subtract the same number from both sides of an equation, it doesn’t effect the equality of the equation.

Multiplication Property of Equality: When you multiply the same number to both sides of an equation, it doesn’t effect the equality of the equation.

Division Property of Equality: When you divide the same number to both sides of an equation, it doesn’t effect the equality of the equation.

* The above four properties are what you do when you solve an Algebraic Equation such as: 2x – 5 = 11 (add 5 to both sides: Addition property of Equality, then divide both sides by 2, Division property of equality).

Substitution Property: If two things are equal you may substitute one for the other: measure of angle 1 = measure of angle 2 and measure angle 2 + measure of angle 3 = 180, since measure of angle 1 = measure of angle 2, I can SUBSTITUTE the measure of angle 1 into my other equation making it: measure of angle 1 + measure of angle 3 = 180.

Transitive Property: (Remember as the 3 piece property) If a = b and b = c then a = c. If the measure of angle 1 = measure of angle 2 and the measure of angle 2 = measure of angle 3, then I know that the measure of angle 1 must also equal the measure of angle 1.

Reflexive Property: (Think Reflection): a=a Something always equals itself. It may seem obvious but is needed in proofs.

Angle Addition Postulate: If you have a big angle divided into two pieces the two pieces add together to equal the total angle.

Corresponding Angles: When two parallel lines are cut by a transversal, the angles that correspond with each other are congruent.

Alternate Interior (and Exterior) Angles: When two parallel lines are cut by a transversal, the angles that are on opposite sides of the transversal line but are both inside (or both outside) the parallel lines) are congruent.

Same Side Interior (and Exterior) Angles: When two parallel lines are cut by a transversal, the angles that are on the same side of the transversal line but are both inside (or both outside) the parallel lines are supplementary.

Remembering Congruence of Angles: Vertical Angles, Corresponding Angles, Alternate Interior (Exterior) Angles
Remembering Supplementary Angles: Linear Pairs, Same Side Interior (Exterior) Angles

These are the vocabulary words one should first learn and also be able to apply to concrete problems and proof situations as they start CCM 2 / Geometry! Good Luck!