rectangle
rhombus
square
'—'
2———•>
trapezoid /_^
secant
tangent
Relations
\
is situated on"
«
point, on line orplane
determines
= congruent (segments, /J$
L\ 's
) — linear sets
\ / lies between (points)
|(
line, in plane
parallel (lines)
perpendicular (lines)
S(a)
"lies on the same side of a"
supl
suplementary to ( 2 /-^ )
vert
vertical to (2 /-'5 )
bis
bisects (pt. bisects seg.j /^>y w /. )
adj.
adjacent (2/.^ 1 2 segments)
comp
complementary to (2 /. 5 )
horn
homologous (parts of congr. figures)
cone
concurrent
inc.
is inscribed in
cire
is circumscribed about
subt
subtend
similar
int
intercepted (/ x by /
X
intersett (2 lines)
)
Objects
point
(A,B,....)
opposite angle (/ )
straight line (l.s.) (a,b,,.,)
/plane)
opposite side (I—-f )
median (l.s.)
linear set - l.s.
altitude (l.s.)
segment (l.s.)
exterior (Interior) angle
extremity (p)
locus (set of pts.)
side of a segment (pl.s.)
midpoint (p)
angle (l.s.) (x,
complement (<L)
triangle (l.s.)
circle (l.s.)
, ....)
supplement (/.)
L. right angle
radius &***)
interior angle (/' )
diameter (1 s.)
exterior angle
chord (l.s.)
alternate
arc (l.s.)
corresponding
inscribed angle
adjacent ^. 's
central angle
transversal (l.s)
ray (l.s.)
center (p)
]_ right angle (/-)
acute angle
rt. A
hypotenuse
leg
obtuse angle
straight angle (/L)
polygon
biscetor (l.s.)
vertex
scalene
perimeter
isosceles
diagonal
equilateral
interior
/ z parallelogram
-3Rules of Thumb
1.
To prove that two segments are equal or two angles are equal, try to prove
them homologous parts of congruent As »
A construction is often necessary for a proof*
It is often necessary to prove one pair ofZJ^> congruent in order to obtain
2/^i or I——*• which are required in turn to prove another pair of ^5
congruent.
2.
To prove two lines (I * try to prove a pair of alternate interior angles.
Use reduotio ad absurdum»==^- <
To prove 2 ^j equal, try to prove that they:
1.
2.
3.
4*
5.
6.
Are homologous^-.* of.—r /Ac> '
Are supplements or complements of same or equal -$ *
Are L. or vert £-<>
Are opposite equal sides of an isosceles
Are alt. -int. or eoryeap.Z.S of transversal
Have sides. I/ or J-
i.e., use theorems.
3*
To prove one segment double another, double the shorter or halve the longer
In solving 2 locus problem, first locate three or more points) then decide
what you think locus is$ then try to prove it is locus - using the
definition.
Construction of triangles
4.
Four segments can be proved proportional by proving them homologous sides
of ,r^
5*
To prove that the product of two segments equals the product of two other
segments, first derive a proportion and then apply (4)*
Constructions
Construction of triangles
Draw a figure representing desired figure - Hake it general
Hark the known parts
Try to determine some part (e.g. A ) that can be constructed
Try to determine how remaining parts can be obtained
Prove that figure satisfied condition
Discuss uniqueness and existence
1.
Construct a triangle
a.
With 3 given sides
2. Bisect an angle
3. Construct an angle at a given pt. of eline-l^a given angle
4. Construct -i- bisector of a given sogaent
5. At a point in a line, construct a-*- to the line.
6. From a point outside a line, construct a ~Jt- to the line.
•7
M
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Ij
To prove t
Theorem goals*
>*/
xT-^
1.
That two -£- 5 are ^ssi
2.
That a line bisects an
3.
That two lines are J— .
4.
That two ^ * are suppl.
5.
That two>u.sare oompl.
6.
That two As are • —- •
?•
That two segments are = .
8.
That two polygons
9. One X* another
10.
A line is unique line with given properties
11.
That two lines are (I .
12.
That three ^-5 a4d to a straight-^-.
13.
That a given point lies on a given line.
14.
That a segment is greater than another.
15.
That three or more lines are concurrent.
it
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