Andrews-Matoka Geometry Review

I apologize profusely for my lack of theorem sheet.
By the way, this contains the correct answers to the true/false, so if you haven't done them, I would do them and check.
*Disclaimer: these are by no means all correct. I probably missed about 10 (max), but Matoka checked my work. Feel free to correct me*
Abbreviations:
Δ=triangle
θ=angle
mθ=measure of angle
ψ=congruent
ω=Parallel
μ=not equal to





















1.F; Commutative Property
2.T; Z is a subset of R
3.T; Ruler Postulate
4.F; Think about R=A
5.T; Hard to describe, but we did it in class (at least on Side B...)
6.F; if the points are all collinear, they only define 1 line.
7.F; If P is 12 inches away from l, and a=.01, then there are 0 points on l that are a away from P.
8.F; lines have no midpoints
9.T; Line Postulate
10.T; See Minimal Incidence Postulate
11.F; Plane Postulate
12.T; Theorem 1-2
13.F; Noncoplanar lines (skew lines) determine no planes
14.????? I'll ask Dr. Hahn
15.F; Think of the Pontiac symbol
16.T; Def'n Convex polygon, Def'n Δ
17.????? I'll ask Dr. Hahn
18.F; a ray will not divide a plane (only a line can)
19.T; No idea what theorem/postulate/definition, suggestion is necessary/helpful
20.????? I'll ask Dr. Hahn
21.????? I'll ask Dr. Hahn
22.T; they must form a triangle for it to work
23.F; this is an extension of 22, from 2D to 3D
24.????? I'll ask Dr. Hahn
25.T; since an angle is 2 rays with a common end point, you get 3 points, determining at least 1 plane
26.T; think parallel lines
27.F; angles w/ measure >90
28.T; Supplementary has no restriction on position, and by def'n supplementary and protractor postulate
29.T; I think it was some theoremcitation needed but, Def'n Supplementary, Def'n congruent angles
30.F; mΘA = mΘB, but ΘΑ does not necessarily equal ΘB.
31.F; ΔABC Ψ ΔMNL (rather than ΔLMN)
32.T; it's possible (if I=X and N=S)
33.F; AAA doesn't work (draw a big eq. Δ and a small eq.Δ)
34.F; by def'n cong. Δ's.
35.T; SAS
36.F; AAS means in that order, so an angle, an angle, and a side, and ASA means the side must be included between the two angles.
37.T; Def'n Δ
38.F; think about true biconditionals
39.T; Obviously.
40.F; I can't draw it here, but if the three angles never intersect
41.T; It's why we can get corollary 1&2 of IΔT and corollary of C-IΔT
42.F; what if C=B
43.T; Def'n Angle bisector
44.F; Think about a straight angle
45.F; 7=5+2 is not a statement (I looked it up in my Humphries notes)
46.T; Look up the supplement theorem
47.T; Since they are the same segments, the endpoints must be the same ( but order doesn't mattter)
48.T; SSS
49.T; SAS
50.F; SSA doesn't always work
51.T; ASA
52.T; AAS
53.F; see 33
54.F; Triangles don't have angle bisectors; unless Dr. Hahn means the “angle bisector of an angle of a triangle”
55.F; ABCD could be a rhombus
56.T; The median of an equilateral triangle
57.F; you have to use 6-2 to get that
58.F; That it has 2 congruent sides can also make it isosceles
59.T; they're logically equivalent (it's how proof by contrapositive works)
60.F; it's just a bisector, not necessarily a perpendicular one
61.F; l can be perpendicular to m
62.F; if A=I, then line AI doesn't exist, since you need 2 points for a line
63.T; Ruler Postulate states that d(a,b)=|a-b|
64.F; Ruler Postulate
65.T; Ruler Postulate
66.F; Minimal Incidence Postulate says that you need 4 noncoplanar points to determine space
67.T; hard to show, but l splits α (the plane) into 2 half-planes. m splits those half-planes into quarter-planes (as long as it intersects l) and thus there are 4 regions
68.F; If A, B, and C are noncollinear
69.F; you can have a different eye color than yourself
70.T; the opposite is the ray that forms a line with the other ray, so if ray AB and ray AC are opposites, they only have A in common, which is 1 point.
71.F; Supplementary puts no restriction on location.
72.????? I'll ask Dr. Hahn
73.????? I'll ask Dr. Hahn
74.F; What if B,D, and A are collinear?
75.F; θBOW and θTIE are congruent, but not necessarily the same angle
76.T; Def'n Δ
77.F; SSA doesn't always work
78.T; otherwise SSA would work
79.T; Def'n median
80.F; take the median from a base angle
81.F;They could be collinear
82.F; That's the minimal Incidence Postulate
83.F; only right triangles. In most triangles, it's called “the longest side”
84.T; Def'n median, def'n midpoints
85.T; one means the existence, and exactly means the uniqueness
86.F; The statement must be false, since the statement and its contrapositive are logically equivalent
87.F; make angleAKE obtuse, then draw the altitude KZ. It doesn't make it isosceles
88.F; What if B=D?
89.F; some medians are perpendicular is the negation (please check this one, definitely)
90.F; it's “greater than or equal to”
91.F; what if D is not the midpoint of segmentAC?

if youre going to post a review, could you at least make it worth it to look at?
im not certain, but im pretty sure that θ doesn't stand for angle

did you make these up or are they from tests and quizzes?

LUke they are (i think) the answers to that giant t/f packet d-hahn gave us

oh ok

Actually paul...
The lower-case letter θ is used as a symbol for:

* A plane angle in geometry.

quoted directly from wikipedia

yes, but that's not what we're using in class, and therefore doesn't matter

that really sucks that you wasted your time making this

ok, i know this is stupid, but is anyone gonna print all the theorems and postulates anyways? cause someone stole my book awhile back so i dont have that....and it would help whoever does it aaallllooootttt

jake, how many important things can you forget/lose. of all subjects to lose your txtbk, math is probably the worst

Do we have to explain for the T and F

She said we migh have to explain a few, and some we wouldn't.

no duh spence, i didnt lose it, some one took it. Andrews, i forgot the sheet dr. hahn gave us so im using yours, i think 61 and 63 are wrong l cant be perpendicular to m and on 63, what if a=b? then its 0, and thats not positive

well paul, as long as people understand what it means, isn't it ok?

Ginger wrote:no duh spence, i didnt lose it, some one took it. Andrews, i forgot the sheet dr. hahn gave us so im using yours, i think 61 and 63 are wrong l cant be perpendicular to m and on 63, what if a=b? then its 0, and thats not positive

Way to blame your problems on other people Jake, typical

way to type something relevant alex

Paul wrote:if youre going to post a review, could you at least make it worth it to look at?
im not certain, but im pretty sure that θ doesn't stand for angle

Actually, Paul, theta is the common use of angles in physics. Don't you remember from vectors (R, theta)? Oh, that's right, you're too impressive to remember. I mean, UNimpressive

thats exactly what i said...