Flashcards

Geometry Chapter 3

Zozan Khoshan English 49 cards

Cards in this deck (49)

1Inductive ReasoningBased on patterns, observations, and assumptions (what you believe to be true but it hasn't been proven).
2Deductive ReasoningBased on facts, definitions, and postulates. It is proven to be true.
3ConjectureAn educated statement that is based on well known information. It is believed to be true but is not yet proven.
4CounterexampleAn example that proves a conjecture to be false. It can be a drawing, statement, or number.
5Conditional StatementAn if-then statement. The original statement. If p, then q.
6HypothesisThe part "p" of a conditional statement following but not including the word "if."
7ConclusionThe part "q" of a conditional statement following but not including the word "then."
8ConverseSwitch the hypothesis and conclusion around. If q, then p.
9InverseAdd "not" in front of the hypothesis and add "not" in front of the conclusion. If not p, then not q.
10Contrapositive"Switch" the hypothesis and conclusion around and add "not" in front of the hypothesis and add "not" in front of the conclusion. If not q, then not p.
11The Conditional Statement (original statement) and the ContrapositiveThe conditional statement and the contrapositive go together, they have the same truth value. Either they are both false or both true.
12The Inverse and the ConverseThe inverse and the converse both go together. They have the same truth value. Either they are both false or both true.
13Bi-conditional StatementBi-conditional statement: "p if and only if q." If the conditional and converse statements are true, then you write a bi-conditional statement.
14Addition POE (Property of Equality)If a = b, then a +c = b + c.
If 4x -2 = 5, then 4x =7. You just have to think to yourself, "How did they get from 4x -2= 5 to 4x =7, well they just added 2." So that is why this is called the "Addition POE!"
15Subtraction POE (Property of Equality)If a = b, then a -c = b -c. If 6x + 2 =5, then 6x = 3. You just have to think to yourself, "How did they get from 6x + 2 = 5 to 6x = 3?" Well they just subtracted 2. " So that is why this is called the "Subtraction POE."
16Multiplication POE (Property of Equality)If a = b, then ac = bc. If x/3= 5, then x=15. You just have to think to yourself, "How did they get 15?" Well, they just multiplied both sides by 3, and that is how they got x = 15. So that is why this is called the "Multiplication POE."
17Division POE (Property of Equality)If a = b, and c does not equal 0, then a/c = b/c. If 2x = 10, then x = 5. You just have to think to yourself, "How did they get from 2x = 10 to x = 5?" Well they just divided by 2, so that is how they got x =5. That is why this is called the "Division POE."
18Distributive POE (Property of Equality)a(b + c)=ab + ac. If 5(x -2) =20, then 5x -10 =20. So you just have to think to yourself, "How did they get from 5(x -2) = 20 to 5x -10 =20?" Well, all they did was multiply 5 to the x and 5 to the -2, so that is how they got 5x - 10 =20. That is why this is called the "Distributive POE."
19Reflexive POE (Property of Equality)When you think of this property, think of when you look in the mirror, you see yourself. You see your reflection. A= A or AB = AB. It equals itself.
20Symmetric POE (Property of Equality)For this property just remember that you flip them around. If a = b, then b = a, all we did was switch or flipped them around.
21Transitive POE (Property of Equality)If a = b and b =c, then a = c. If x =2 and 2 =y, then x = y.
22Substitution POE (Property of Equality)If a = b, then b can be substituted for a in any expression. For this property you are just replacing something. If x =5 and 20 = x + 15, then we have 20 = 5 + 15. So all we did was replace the x with the number 5.
23Reflexive POC (Property of Congruence)Figure A is congruent to Figure A. Segment AB is congruent to Segment AB. For this property just think reflection and looking in the mirror you see yourself.
24Symmetric POC (Property of Congruence)If figure A is congruent to figure B, then figure B is congruent to figure A. If angle A is congruent to angle B, then angle B is congruent to angle A.
25Transitive POC (Property of Congruence)If figure A is congruent to figure B and figure B is congruent to figure C, then figure A is congruent to figure C. If angle A is congruent to angle B and angle B is congruent to angle C, then angle A is congruent to angle C.
26Definition of MidpointIf a point is a midpoint, then it divides a segment into two congruent parts.
27Definition of Supplementary AnglesIf two angles are supplementary, then they have a sum of 180 degrees.
28Definition of Complementary AnglesIf two angles are complementary, then they have a sum of 90 degrees.
29Definition of Angle BisectorIf a segment is bisected, then it is divided into two congruent angles. Remember the word "Bisect" means to cut into two equal parts.
30Definition of Segment BisectorIf a segment is bisected, then it is divided into two congruent segments. Remember the word "Bisects" means to cut into two equal parts.
31Definition of PerpendicularIf lines form right angles at their intersection (the word intersection means they cross each other) then they are perpendicular.
32Definition of CongruenceIf two figures are congruent, they they have the same measure or length.
33Definition of Right AngleIf an angle is right, then it measures 90 degrees.
34Segment Addition PostulateIf B is between A and C, then AB + BC = AC.
35Angle Addition PostulateIf X is in the interior of angle ABC, then the measure of angle ABX + the measure of angle XBC = the measure of angle ABC.
36Linear Pairs TheoremIf two angles form a linear pair, then they are supplementary.
37Vertical Angles TheoremIf two angles are vertical, then they are congruent.
38Right Angles Congruence TheoremAll right angles are congruent.
39Congruent Supplement TheoremIf two angles are supplementary to the same angle then the two angles are congruent.
40Congruent Complements TheoremIf two angles are complementary to the same angle, then the two angles are congruent.
41SegmentThe part of a line that connects two points. Basically it is a line that has two endpoints.
42CongruentThe same shape and size. Angles are congruent when they are the same size in degrees. Sides are congruent when they are the same length.
43Acute AngleIt is less than 90 degrees.
44Right AngleEquals exactly 90 degrees.
45Obtuse AngleIt is greater than 90 degrees but less than 180 degrees.
46Straight AngleEquals exactly 180 degrees.
47Vertical AnglesVertical Angles are the angles opposite each other when two lines cross.
48Complementary AnglesTwo angles are Complementary when they
add up to 90 degrees.
49Supplementary AnglesTwo Angles are Supplementary when they add up to 180 degrees.