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Guided Notes for Chapter 5
Lesson 5.1 Polygon Sum Conjecture
Quadrilateral Sum Conjecture
The sum of the measures of the four angles in any quadrilateral is
.
Pentagon Sum Conjecture
The sum of the measures of the five angles in any pentagon is
.
Polygon Sum Conjecture
The sum of the measures of the n angles of an n-gon is
.
Lesson 5.2 Exterior Angles of a Polygon
Exterior Angle Sum Conjecture
For any polygon, the sum of the measures of a set of exterior angles is
.
Equiangular Polygon Conjecture
You can find the measure of each interior angle of an equiangular n-gon
by using either of these formulas:
.
Lesson 5.3 Kite and Trapezoid Properties
The two angles between each pair of congruent angles of a kite are the
angles of the kite. The other pair of angles are called the
angles.
Kite Angle Conjecture
The
angles of a kite are
Kite Diagonals Conjecture
The diagonals angles of a kite are
.
.
Kite Diagonal Bisector Conjecture
The diagonal connecting the vertex angles of a kite is the
of the other diagonal.
Kite Angle Bisector Conjecture
The
angles of an kite are
by a diagonal.
A trapezoid is a quadrilateral with exactly one pair of
sides.
The parallel sides are called
. A pair of angles that share a
base as a common side are
angles.
Trapezoid Consecutive Angles Conjecture
The consecutive angles between the bases of a trapezoid are
.
Isosceles Trapezoid Conjecture
The base angles of an isosceles trapezoid are
Isosceles Trapezoid Diagonals Conjecture
The diagonals of an isosceles trapezoid are
.
.
Lesson 5.4 Kite and Trapezoid Properties
Three Midsegments Conjecture
The three midsegments of a triangle divide it into four
.
Triangle Midsegment Conjecture
A midsegment of a triangle is
length of the
side.
to the third side and
Trapezoid Midsegment Conjecture
The midsegment of a trapezoid is
to the bases and is
length to the
of the lengths of the bases.
the
in
Lesson 5.5 Properties of Parallelograms
Parallelogram Opposite Angles Conjecture
The opposite angles of a parallelogram are
.
Parallelogram Consecutive Angles Conjecture
The consecutive angles of a parallelogram are
Parallelogram Opposite Sides Conjecture
The opposite sides of a parallelogram are
Parallelogram Diagonals Conjecture
The diagonals of a parallelogram
A
.
.
.
is a quantity that has both magnitude and direction.
The
vector of multiple vectors is a single vector that has the
same effect and is called a
.
Lesson 5.6 Properties of Special Parallelograms
Double-edged Straightedge Conjecture
If two parallel lines are intersected by a second pair of parallel lines that
are the same distance apart as the first pair, then the parallelogram
formed is a
.
Rhombus Diagonals Conjecture
The diagonals of a rhombus are
.
and they
Rhombus Angles Conjecture
The
of a rhombus
A
the angles of the rhombus.
is an equiangular parallelogram.
Rectangle Diagonals Conjecture
The diagonals of a rectangle are
Square Diagonals Conjecture
The diagonals of a square are
.
and
,
.
, and