Transcript 2nd Term Conjectures

2nd Term Conjectures
Triangle Congruence 2  are :

SSS  conj if all 3 sides are 
SAS  conj if 2 sides and the  between those 2 sides are 

ASA  conj if 2 s and the side between them are 

SAA  conj if 2 s and the side not between them are 

*CPCTC
Vertex Angle Bisector Conj

In an ISOSCELES , the bisector of the
vertex  is also the altitude to the base
and the median to the base.
Additional Conj






Right  Conj – All right s are .
Complements of  s are .
Supplements of  s are .
 Supplements Conj – If 2 s are both
 & supplementary, then each  is
right.
Common Segment Conj
Common Angle Conj
Conj on Polygons
Polygon Sum Conj – The sum of the
measures of the n angles of an n-gon is
180(n
– 2)
_________.
 Exterior  Sum Conj – The sum of the
measures of ONE set of exterior s is
360o
____.
*n-gon terms

Kite Properties




Kite Diagonals Conj – The diagonals are .
Kite Diagonal Bisector Conj – The diagonal
connecting the vertex s of a kite is the 
bisector of the other diagonal.
Kite s Conj – The nonvertex s of a kite
are .
Kite  Bisector Conj – The vertex s are
bisected by a diagonal.
Trapezoid Properties
+ = 180o



Trap Consecutive s Conj – The
consecutive s between the bases of a
trap. are supplementary.
ISOSCELES Trap Conj
– The base s are .
ISOSCELES Trap Diagonals Conj
– The diagonals are .
Midsegment Properties

 Midsegment Conj – A midsegment of a  is
// to the 3rd side and half the length of the
3rd side.
a/2
a

Trap Midsegment Conj
– The midsegment of a trap. is // to
the bases and is equal in length to
the average of the 2 base lengths.
a
(a+b)/2
b
//ogram Properties






2 pairs of opposite sides are //. (by defn.)
2 pairs of opposite sides are .
2 pairs of opposite s are .
2 pairs of consecutive interior s are
supplementary.
One pair of opposite sides is // and .
The diagonals bisect each other.
Rhombus Properties


Rhombus Diagonals Conj - The diagonals
are  bisectors of each other.
Rhombus Angles Conj - The diagonals
bisect the angles of the rhombus.
Rectangle Properties


The measure of each  of a rectangle is 90o.
Rectangle Diagonals Conj - The diagonals of
a rectangle are .
Square Properties

Square Diagonals Conj

The diagonals of a square are ,  and bisect
each other.
 Chords in a Circle

If 2 chords are , then:
 they determine
2 central s that are .


their intercepted arcs are .
2  chords are
equally distant
from the center.
●
●
●
s in a Circle


The  from the center to a chord
is the  bisector of the chord.
●
The  bisector of a chord passes through
the center.
●
Tangent Properties


Tangent Conj – A tangent to a circle is
 to the radius drawn to the point of
tangency.
Tangent Segments Conj – Tangent
segments to a circle from a point
outside the circle are .
●
●
Inscribed s


Inscribed  Conj – The measure of an
inscribed is half the measure of the arc
it intercepts.
a/2o
ao
The inscribed s that intercept the same arc are .

ao
ao
2ao
s inscribed in a semicircle
are right.
ao
Other Conj on Circles
ao


The opposite s of a quadrilateral
inscribed in a circle (cyclic quad) are
supplementary.
Parallel lines intercept  arcs in a circle.
Vertex is outside the circle
a b
x
2
Intersecting Tangents and Secants Conj.
The measure of an angle formed by
either secants, tangents or both is half the
difference of the larger intercepted arc measure
and the smaller intercepted arc measure.
Vertex is inside the circle
ab
x
2
Intersecting Chords Conj.
The measure of an angle formed by
two intersecting chords is half the
sum of the two intercepted arcs.
Vertex is on the circle
a
x
2
Tangent – Chord Conj.
The measure of an angle formed by the
intersection of a tangent and a chord at
the point of tangency is half the measure
of its intercepted arc.
Conj/Defn/Properties
Used in Proving






Reflexive Property
Vertical Angles Conj
Defn of a Linear Pair; Linear Pair Conj
Parallel Lines Conj & their Converse
 AIA (), AEA(), CA(), CIA (suppl)
Defn of Isosceles 
Isosceles  Conj & its Converse
Conj/Defn/Properties
Used in Proving







Defn of Midpoint, Median
Defn of  Bisector, Segment Bisector,
 Bisector
Defn of  Lines
 Sum Conj
 Exterior  Conj
3rd Angle Conj
Transitive Property, APE, MPE
Formula




Distance Formula (~ Eqn of a Circle)
Midpoint Formula
Pythagorean Thm
Special Right Triangles


90-45-45 (Isosceles Right )
90-30-60