Download Geometry Chapter:Quadrilateral Review Problems

Geometry Chapter:Quadrilateral
Review Problems
Do any 40 of the problems listed for 10pts on the test. Do any
additional listed problems for 1/4 pt of extra credit each
pp. 813-814 #10-16,25-30,40
p. 823 # 1, 7, 16
Attached problems below:
13. Copy and complete the table below by placing a yes (to mean always) or a no (to mean
not always) in each empty space. Use what you know about special quadrilaterals.
Opposite sides
are paf3l1el
Opposite sides
are congruent
Opposite angles
are congruent
Diagonals bisect
each other
Diagonals are
perpendicular
Diagonals are
congruent
Exactly one line
of symmetry
Exactly two lines
of symmetry
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Isosceles
Kite
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I
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Yes
7. Find x and y.
I trapezoid I Paf3l1elogram
I
I
I
I
,
I
I
I
I
I
I
I
I
I
I
I Rhombus
I Rectangle I
I
I
I
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I
1
\
,
i
I
I
I
I
I
I
I
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No
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I
j
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8. Perimeter
Find x.
I
I
= 266 em.
9. Find a and c.
50°
10. ,\-15 is a midsegment. Find
11. Find x.
12. Find Y and
=.
the perimeter of MOIS.
I
G
·As
~r
o
.\1
2b
,
i
x- 12
:32 em
I
x
-----,.
CMsmIcriDn In Exercises 21 ~24, use the ~ segments and angles to consUUct each
~ el·th er pa
tty p'aper or a compass and a straightedge. The small lener above
figure. Tv5e
each segment represents the length of the segment.
\'
I
:
21. ConstrUct rhombus SQRE
with SR = Y and QE = x.
22. Construct kite FLYR given
LF. LL, and FL = x.
F£----------­
23. Given basesLP with length Z
I
and £.'\J with length y. nonparallel
.
with length x. and LL. construct trapezoid PENL. ®
side
u:
25. Three regular polYgons meet at point B. OnJv
four sides of the third polygon are visible. .
How many sides does thIS poiygon have?
-
26. Find x.
I
~
.
,
.
..'~ ", B
27.
P~ove the conjeCture: The diagonals of a rhombus
bisect the angles.
Given: Rhombus DE.\'1. with diagonal D.\'
ShOW: Diagonal DS bisects .::....D and LN .
Flowchart Proof
/' .2,
j
N
Df= '
Pr.:-DE- -N-h -,(.--',1
'
,..----
D'---'-----..J
\
a rnombw
" rr-='3----.1
NE
=='
r;-------,
1-15. ,
/
- -
=r
,-;
'6
- - --'- 1 _ .. Ll ==
\
r.,.,:------
.:..1.. :-1 ...
":'3==!...l.~
1. How do you find the measure of one exterior angle of a regular
poiygon?
2. How can you find the number of sides of an equiangular polygon by m:..asuring one
ot" its interior angles? By measuring one of its exterior angles?
­
6. How can you use the Triangle Midsegmcm Coniecture to find a distance between
two pOints that you can't measure directly?
DN bisectS
_
ID­
~ and ~I,VE
~
Find the sum of the measures of the interior angles of the convex polygon
I. decagon
2. . 16-gon
Find the value of x.
'1.
Find the value of x.
You are given the measure of each interior angle of a regular
n-gon. Find the value of n.
(nx - 17l c
'-:::::;
I
(2x _
Ql"
You are given the measurF of each exterior angle of a regular
n-gon. Find the value of n.
15. Find ,the measure of each lettered angle.
8.
7- ..0=
36
C
In Exercises 34-56. identify' the statement as true or
false. For each false statement, explain why it is false or
sketch a counterexampie.
36. The diagonals of a parallelogram are congruent.
0
37. The measure of each angle of a regular dodecagon is 150
•
39. If CD is the midsegment of trapezoid PLYR with PL one of the bases. then
CD
= +(PL +
YR).
41. If the sum of the measures of the interior angles of a polygon is less than 1000°.
then the polygon has fewer than seven sides.
-of -exterior angles of a polygon is alway,,- less
43. The sum of the measures 0 f one se
t
than the sum of the measures of interior angles.
44. Both pairs of base angles of an isosceles trapezoid are supplementary.
45. If the base angles of an isosceles triangle each measure 48°, then the vertex angle has
a measure of 132°.
48. The diagonals of a rhombus bisect the angles of the
rhombus.
49. The diagonals of a rectangle are perpendicular bisectors
of eaeh other.
'
51. If a quadrilateral has three' congruent angles. then it is a
.rectangle.
54. If the sum of the lengths of two consecutive sides of a
kite is 48 em. then the perimeter of the kite is 96 ern.