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Geometry
Chapter 6 Study Guide (6.1-6.6)
Polygons and Quadrilaterals
Vocabulary
side of a polygon - each segment that forms a polygon
vertex of a polygon - endpoint of two sides
diagonal - a segment that connects any two nonconsecutive vertices
regular polygon - a polygon that is both equilateral and equiangular
concave - a polygon with a diagonal containing points exterior to the polygon
convex - a polygon in which no diagonal contains points exterior to the polygon
parallelogram - a quadrilateral with two pairs of parallel sides
kite - a quadrilateral with exactly two pairs of congruent consecutive sides
trapezoid - a quadrilateral with exactly one pair of parallel sides
• base - a parallel side in a trapezoid
• base angles - two consecutive angles whose common side is the base of a trapezoid
• leg - a nonparallel side in a trapezoid
Theorems, Postulates, and Properties
• Polygon Angle Sum Theorem - The sum of the interior angle measures of a convex polygon with n sides is (n-2)180˚.
• Polygon Exterior Angle Sum Theorem - The sum of the exterior angle measures, one angle at each vertex, of a
convex polygon is 360˚.
• Properties of a parallelogram:
• opposite sides are congruent.
• opposite angles are congruent.
• consecutive angles are supplementary.
• diagonals bisect each other.
• Conditions for parallelograms: a quadrilateral in which
• one pair of opposite sides are parallel and congruent.
• both pairs of opposite sides are congruent.
• both pairs of opposite sides are parallel.
• both pairs of opposite angles are congruent.
• an angle is supplementary to both of its consecutive angles.
• the diagonals bisect each other.
• Properties of a kite: a quadrilateral in which
• its diagonals are perpendicular
• exactly one pair of opposite angles are congruent
• If a quadrilateral is an isosceles trapezoid, then each pair of base angles are congruent.
• If a trapezoid has one pair of congruent base angles, then it is an isosceles triangle.
• A trapezoid is isosceles if and only if its diagonals are congruent.
• Trapezoid Midsegment Theorem - The midsegment of a trapezoid is parallel to each base,
and its length is one half the sum of the lengths of the bases.
Geometry
Chapter 6 Practice Problems
1) Any regular polygon can be inscribed in a circle. Find
the length of a side of the regular octagon in terms of r.
Name: ______________________________________
Date: ____________________ Period: ____________
2) A campground site is in the shape of a convex
quadrilateral. Three sides of the campground form two
right angles. The third interior angle measures 10˚ less
than the fourth angle. Find the measure of each interior
angle.
!
side length of regular octagon = __________________
Interior angles = _____________________________
3) Quadrilateral ABCD has midpoints E, F, G, and H.
Show that the area of EFGH is half the area of ABCD.
4) In parallelogram EFGH, FH = 5x
inches, EG = (2x+4) inches, and JG =
8 inches. What is the length of JH?
!
JH = _________________________
5) The graphs of y = 2x, y = 2x - 5, and y = -x in the
coordinate plane contain three sides of a quadrilateral.
Find the equation of the line whose graph contains a
segment that can complete the quadrilateral and form a
parallelogram.
6) Show that the quadrilateral with vertices E(-1, 5), F(2,
4), G(0, -3), and H(-3, -2) is a parallelogram.
7) What is the length of the midsegment of trapezoid
ADEB in inches?
8) Construct a kite such that AC is the segment that
connects the congruent angles.
!
A
midsegment length = __________
C