GT Geometry
Unit 6:
Quadrilaterals
Jeopardy
Angles of
Polygons
|| - ogram
Properties
|| - ogram
Tests
Rhombi/Tra
pezoids
Area
Coordinate
Plane
100
100
100
100
100
100
200
200
200
200
200
200
300
300
300
300
300
300
400
400
400
400
400
400
500
500
500
500
500
500
$100
What is the sum of the interior
angles of a pentagon?
$100
540 Degrees
$200
What is the measure of each
exterior angle of a regular
octagon?
$200
45 degrees
$300
If each interior angle of a
regular polygon is 140
degrees how many sides
does the polygon have?
$300
9 sides
$400
If each exterior angle of a
regular polygon is 72
degrees how many sides
does the polygon have?
$400
5 sides
$500
If each interior angle of a
regular polygon is 150
degrees what is the measure
of each exterior angle?
$500
30 degrees
$100
Find x if the quad below is a
parallelogram
$100
X=7
$200
Find x if the quad below is a
parallelogram
$200
X = 12
$300
Find x if the quad below is a parallelogram
$300
X=3
$400
Find x if the quadrilateral below is a
parallelogram
$400
X= 33
$500
Find x if the quadrilateral below is a
parallelogram
$500
X = 14.5
$100
Can we prove this quadrilateral is a
parallelogram?
$100
Yes both pairs of opposite
sides are congruent
$200
Can we prove this quadrilateral is a
parallelogram?
$200
No, we don’t know that both
pairs of opposite angles are
congruent
$300
Can we prove this quadrilateral is a
parallelogram?
$300
Yes, one pair of opposites
sides is both congruent and
parallel
$400
Can we prove this quadrilateral is a
parallelogram?
$400
Yes, diagonals bisect each
other
$500
Can we prove this quadrilateral is a
parallelogram?
$500
Yes, the total sum of the angles of a
quadrilateral is 360 degrees. Therefore x =
100. Since the opposite angles are
congruent it is a parallelogram
$100
If the quadrilateral below is a rhombus, find x
$100
X = 4.5
$200
If the trapezoid below is an isoceles trapezoid
find x.
$200
X = 12
$300
If the trapezoid below is an isosceles
trapezoid, find x
$300
X = 14.5
$400
If the quadrilateral below is a rhombus find x
$400
X=2
Diagonals of a rhombus
bisect angles
$500
If the quadrilateral below is a rhombus find x
$500
X = 17
The diagonals of a rhombus
are perpendicular so use the
Pythagorean theorem
$100
Find the area of the polygon
$100
A = 70
Area of a rhombus = ½ (d1)(d2)
D1 = 7 + 7 = 14
D2 = 5+5 = 10
$200
Find the area of the quadrilateral
$200
A = 64
Area of a trapezoid = ½ (b1+b2)h
= ½ ( 6+10) 8
$300
Find the area of the quadrilateral
below. Hint (use the Pythagorean
theorem to find the missing side.)
$300
A = 192
The height of the rectangle = 12.
12 x 16 = 192
$400
The quadrilateral has an area of 60
sq inches. Find x
$400
x=8
$500
Find the area of the yellow region.
$500
X = 96.
The area of the rectangle = 16 x 12. The area of
the two triangles are ½ (8)(12). Subtract the
two.
$100
JKLM is a quadrilateral with
J(0,0), K (3,7), L(9,7) and M(6,0).
Is JKLM a parallelogram?
$100
Yes opposite sides are parallel and congruent
Slope:
JK = 7/3
LM = 7/3
KL = 0
JM = 0
$200
Is ABCD a rhombus?
A (3,1) B(3,-3) C(-2,-3) D (-2,1)
$200
No. Diagonals are not perpendicular
Slope of diagonals
AC = 4/5
BD = - 4/5
$300
Is LMNO a trapezoid?
L ( 5,2) M (1,9) N (-3, 2)
O (1,-5)
$300
Yes. 1 opposite side is parallel. It is also an
isosceles trapezoid.
Slope
LM = - 7/4
ON = -7/4
Congruent Legs
LO = sq rt 65
MN = sq rt 65
$400
Is PQRS a square?
P (5,2)
Q (2,5)
R( -1,2)
S (2,-1)
$400
Yes. Diagonals are congruent and
perpendicular
Congruent
RP = 6
QS = 6
Slope
RP = 0
QS = undefined.
$500
JKLM is a quadrilateral with
K(6,0) L (7,2) and M (2,8) what are the
coordinates of J to make JKLM a
parallelogram?
$500
J = (1,6) or (11,-6)
The slope of LM = -6/5. Therefore the slope of JK = -6/5. The slope could
also be written as 6/-5. Therefore we must solve for x and y. The
following two coordinates would make this slope (1,6) or (11,-6)
y–0=6
x = 1, y = 6
y – 0 = -6
x = 11, y = -6
x – 6 = -5
x–6=5
Then we find that the distance for LM = sq rt 61. Therefore, we plug in
both possible coordinates to determine which one gives us a distance
for JK = sq rt 61. Since they both do both answers are correct.
JK when J = (1,6) = sq rt 61
JK when J = 11,-6) = sq rt 61