Ch 5 Summary with Tree Diagram Key
Name ____________________________
Chapter 5: Discovering and Proving Polygon Properties
Properties of Polygons
Properties of Regular Polygons
The sum of its interior angles is 180(n – 2).
The sum of the exterior angles is 360.
n ( n − 3)
diagonals.
Polygon of n sides has
2
The measure of each interior angle is
( n − 2)180
360
180
−
or
n
n
The measure of each exterior angle is 360/n.
Midsegment (of a triangle) is the line segment
connecting the midpoints of two sides of the triangle.
The three midsegments of a
triangle divide it into four
congruent triangles.
A midsegment of a triangle is
parallel to the third side and
half the length of the third side.
Midsegment (of a trapezoid) is the line
segment connecting the midpoints of the two
nonparallel sides.
The midsegment of a
trapezoid is:
parallel to the bases and
equal in length to the average
of the lengths of the bases.
Ch 5 Summary with Tree Diagram Key
Name ____________________________
Quadrilateral
Def.: A four-sided polygon.
Sum of the interior angles is 360.
Kite
Def.: A quad. with exactly two distinct
pairs of consecutive congruent sides.
The nonvertex angles are congruent.
The diagonals are perpendicular.
The diagonal between the vertex
angles bisects the other diagonal.
It has exactly one line of symmetry.
Parallelogram
Def.: A quad with [both pairs]
opposite sides parallel.
Trapezoid
Opposite sides are congruent.
Opposite angles are congruent.
Consecutive angles are supplementary.
Diagonals bisect each other.
Consecutive angles between
the bases are supplementary.
Rhombus
Rectangle
Def.: An equilateral parallelogram [4 sides congruent].
Def.: An equiangular parallelogram.
Diagonals are perpendicular bisectors of each
other.
Diagonals bisect the opposite pairs of angles.
It has two lines of symmetry and 2-fold
rotational symmetry.
Each angle measures 90 [all right
angles].
Diagonals are congruent.
It has two lines of symmetry and
2-fold rotational symmetry.
Def.: A quad with exactly one pair
of parallel sides.
Isosceles Trapezoid
Def.: A trapezoid whose 2
nonparallel sides are the same
length.
Base angles are congruent.
Diagonals are congruent.
Has one line of symmetry.
Square
Def.: An equiangular rhombus or an equilateral rectangle.
It has four lines of symmetry and
4-fold rotational symmetry.