Transcript Chapter 6

Chapter 6
Polygon Properties
C-38 The sum of the measures of the four
angles of every quadrilateral is 360
(Quadrilateral sum conjecture)
C-39 The sum of the measures of the n angles
or an n-gon is 180(n-2) (Polygon sum
Conjecture)
Lesson 6.2
C- 40 The sum of the measures of one set of
exterior angles is 360° (Exterior Angle sum
Conjecture)
C-41 The measure of each angle of an
equiangular n-gon can be found by using either
of the following expressions:
360
180 
n
(n  2)180
n
Number of sides of
polygon
3
4
5
6
7
8
9
10
Sum of measures
of angles
180
360
540
720
900
1080
1260
1440
each angle in a
regular
60
90
108
120
128.6
135
140
144
Exterior angles
360
360
360
360
360
360
360
360
Lesson 6.3
Kite – a quadrilateral with exactly two pairs
of distinct congruent consecutive sides.
C-42 The diagonals of a kite are
perpendicular (Kite Diagonals conjecture)
C-43 The diagonal connecting the vertex
angles of a kite is the perpendicular
bisector of the other diagonal (Kite
diagonal bisector conjecture)
C – 44 The nonvertex angles of a kite are
congruent (Kite angles conjecture)
C – 45 The vertex angle of a kite are
bisected by a diagonal (Kite angle bisector
conjecture)
Trapezoid – a quadrilateral with exactly
one pair of parallel sides
C – 46 The consecutive angles between
the bases of a trapezoid are
supplementary (Trapezoid consecutive
angles Conjecture)
C – 47 The base angles of an isosceles
trapezoid are congruent (Isosceles
trapezoid conjecture)
C-48 The diagonals of an isosceles
trapezoid are congruent (Isosceles
Trapezoid Diagonals conjecture)
Lesson 6.4
Midsegment – segment connecting the
midpoints of two sides of a triangle
C – 49 The three midsegments of a
triangle divide the triangle into four
congruent triangles.
C – 50 A midsegment of a triangle is
parallel to the third side and half the length
of the third side. (Triangle midsegment
conjecture)
C – 51 The midsegment of a trapezoid is parallel
to the bases and is equal in length to the
average of the two base lengths (Trapezoid
Midsegment conjecture) m EF = 3.80 cm
1
(b1  b2 )
2
m DA = 2.86 cm
m CB = 4.74 cm
D
F
C
A
E
B
Lesson 6.5
Parallelogram – a quadrilateral whose
opposite sides are parallel.
C–52 The opposite angles of a
parallelogram are congruent.
C–53 the consecutive angles of a
parallelogram are supplementary.
C -54 The opposite sides of a
parallelogram are congruent.
C – 55 The diagonals of a parallelogram
bisect each other.
Vector – a ray that has direction and
magnitude.
Lesson 6.6
C – 56 If two parallel lines are intersected
by a second pair of parallel lines the same
distance apart as the first pair, then the
parallelogram formed is a rhombus.
C – 57 The diagonals of a rhombus are
perpendicular bisectors of each others.
C – 58 The diagonals of a rhombus bisect
the angles of the rhombus.
Rectangle – an equiangular parallelogram.
C-59 The measure of each angle of a
rectangle is 90°
C-60 the diagonals of a rectangle are
congruent.
Square – an equiangular rhombus.
Square – an equilateral rectangle.