Geometry--Ch. 6 Review
Classify each polygon as regular/irregular, concave/convex,
and name it based on its number of sides:
1)
2)
irregular
concave
decagon
regular
convex
pentagon
Geometry--Ch. 6 Review
3)
Find the value of x:
148o
108o
xo
112o
Since the figure is a pentagon,
the interior angle sum must be 540o.
Angle Sum = (5-2)(180) = 540
87o
o
These four angles add up to 455o.
x = 540 - 455
x = 85o
Geometry--Ch. 6 Review
4)
Find the value of x:
128o
4x-3o
Since the figure is a hexagon,
the interior angle sum is 720o.
o
These angles add up to 362 .
4x
3x+20o
116o
o
118o
Therefore, the remaining angles must add up to 358o.
(4x-3) + (3x+20) + 4x = 358
11x + 17 = 358
11x = 341
x = 31
Geometry--Ch. 6 Review
5)
Find the interior angle sum for a convex septagon:
ANSWER:
Since a septagon has seven sides, we insert a 7 into
the interior angle sum formula.
Angle Sum = (n - 2)(180)
Angle Sum = (7-2)(180)
Angle Sum = (5)(180)
900 degrees
Geometry--Ch. 6 Review
6) The sum of the measures of six angles in a convex
octagon is 969o. The 7th angle is twice as large as the
8th angle. Find the measures of both missing angles:
ANSWER:
Since an octagon has eight sides, we know that the
sum of its interior angles should be 1080 degrees.
Angle Sum = (8-2)(180) = 1080
Since six of the angles add up to 969 degrees, the
remaining two angles must add up to 111 degrees.
1080 - 969 = 111
Geometry--Ch. 6 Review
6) The sum of the measures of six angles in a convex
octagon is 969o. The 7th angle is twice as large as the
8th angle. Find the measures of both missing angles:
The remaining 111o must be divided into 3 equal parts.
The reason for this is because one angle is twice as
large as the other.
7th angle
2x
8th angle
x
+
3x
x
=
111
=
111
=
37
7th angle
8th angle
7th angle
8th angle
2(37)
74
o
(37)
37
o
Geometry--Ch. 6 Review
7)
A regular convex polygon has 12 sides. Find the
measure of each interior angle and each exterior angle:
ANSWER:
Since the exterior angles always have to add up to
360, each exterior angle would have to be...
360/12 = 30o
Since the interior and exterior angles always
combine to form linear pairs, each interior angle
would have to be...
180 - 30 = 150o
Geometry--Ch. 6 Review
8)
Each interior angle of a regular convex polygon
measures 144 degrees. How many sides does the
polygon have?
ANSWER:
If each interior angle is 144 degrees, then each
exterior angle would have to be 36 degrees.
180 - 144 = 36
If each exterior angle is 36 degrees, then the
polygon is a decagon with 10 sides.
360/36 =
10 sides
Geometry--Ch. 6 Review
9)
Find the area of an equilateral triangle with sides
of 14 cm:
ANSWER:
If you drop an altitude down
from the vertex angle, two
30/60/90 triangles are formed.
14 cm
14 cm
14 cm
From last chapter, we know the
length of the altitude is 7 3 .
14 cm
Area = (½)(14)( 7 3 )
Area = 49 3 cm2
73
7 cm
Geometry--Ch. 6 Review
10)
Name the four properties of all parallelograms:
~Both pairs of opposite sides are congruent.
~Both pairs of opposite angles are congruent.
~Consecutive angles are supplementary.
~Diagonals bisect each other.
Geometry--Ch. 6 Review
11)
Find x and y in the parallelogram shown:
3x+4
Opposite sides must be congruent.
5x - 9 = 3x + 4
2x - 9 = 4
2x = 13
6y+8o
11y+1o
5x-9
x = 6.5
o
If 11y
x = +6.5,
then
this
angle
would
be
47
.
1 = 133
Since consecutive
angles must be supplementary,
11y = 132
this angle would be 133o.
y = 12
Geometry--Ch. 6 Review
12)
Find x, y, and z in the parallelogram shown:
Like all triangles, this one’s
Opposite angles must beo ≅.
angles add up to 180 .
3x + 5 = 53
53 + 43 + 2y = 180
3x = 48
x = 16
2y
3x+5o
o
53
o
53o
2x+11o
zo
43o
o
If
x
=
16,
then
this
angle
is
43
.
y
=
42
2y = 84
In a parallelogram, alternate interior angles are ≅.
z = 43
Geometry--Ch. 6 Review
Do the following quadrilaterals have to be
parallelograms? If so, why?
13)
YES; Both pairs of
opposite sides are ≅.
15)
14)
NO; We need BOTH
pairs of opposite
angles to be ≅.
YES; The same pair
of opposite sides is
parallel and ≅.
Geometry--Ch. 6 Review
16)
Find the missing angles in the following rhombus:
Opposite angles are ≅.
Since consecutive angles are
supplementary, these large
angles are each 112o.
In a rhombus, diagonals bisect the
opposite angles. Therefore, both
112o angles get split into four
different 56o angles.
56o 1 2
o
68
56o
5
3
56o
4
56o
68o
Geometry--Ch. 6 Review
17)
Given the following trapezoid and its midsegment,
find the value of x:
2x + 8 15
9 units
(2x+8) + (8x+5) = 2 (6x+3)
6x + 3
8x + 5
24
apart
33
10x + 13 = 12x + 6
13 = 2x + 6
7 = 2x
x = 3.5
By plugging the x = 3.5
back in, we can see that
we’re correct.
Geometry--Ch. 6 Review
18)
Find the missing angles in the following kite:
Kites have one pair of opposite angles ≅.
So angles T & E are both 107o.
Since the angle sum of a triangle
is 180o, m∠2 = 31o.
G
42o 4
T
The two triangles in the kite
are ≅ (by SSS). Therefore, we
know the other missing angles as well.
42o
E
107o 3
107o
o
31o 1 2 31
M
Geometry--Ch. 6 Review
TRUE or FALSE?
19)
The diagonals of a rectangle are congruent.
TRUE
20)
The diagonals of a trapezoid bisect each other.
FALSE
21)
All rhombuses are squares.
(The converse is true.)
FALSE
22)
All parallelograms are quadrilaterals.
TRUE