Geometry--Ch. 6 Review

1
Geometry--Ch. 6 Review
Classify each polygon as regular/irregular,
concave/convex,and name it based on its number
of sides
irregularconcavedecagon
regularconvexpentagon
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Geometry--Ch. 6 Review
3) Find the value of x
Since the figure is a pentagon,the interior
angle sum must be 540o.
Angle Sum (5-2)(180)
540o
These four angles add up to 455o.
x 540 - 455
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Geometry--Ch. 6 Review
4) Find the value of x
Since the figure is a hexagon,the interior angle
sum is 720o.
(4x-3) (3x20) 4x 358
11x 17 358
11x 341
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Geometry--Ch. 6 Review
5) Find the interior angle sum for a convex
septagon
ANSWERSince 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
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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
ANSWERSince 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.
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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.


111
3x 111
x 37
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Geometry--Ch. 6 Review
7) A regular convex polygon has 12 sides.
Find the measure of each interior angle and each
exterior angle
ANSWERSince 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
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Geometry--Ch. 6 Review
8) Each interior angle of a regular convex
polygon measures 144 degrees. How many
sides does the polygon have?
ANSWERIf 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
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Geometry--Ch. 6 Review
9) Find the area of an equilateral triangle
with sides of 14 cm
ANSWERIf you drop an altitude down from the
vertex angle, two 30/60/90 triangles are formed.
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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.
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Geometry--Ch. 6 Review
11) Find x and y in the parallelogram shown
Opposite sides must be congruent.
5x - 9 3x 4
2x - 9 4
2x 13
x 6.5
11y 1 133
11y 132
y 12
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Geometry--Ch. 6 Review
12) Find x, y, and z in the parallelogram shown
Like all triangles, this onesangles add up to
180o.
Opposite angles must be ?.
3x 5 53
53 43 2y 180
3x 48
x 16
If x 16, then this angle is 43o.
y 42
2y 84
In a parallelogram, alternate interior angles are
?.
z 43
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Geometry--Ch. 6 Review
Do the following quadrilaterals have to be
parallelograms? If so, why?
YES Both pairs ofopposite sides are ?.
NO We need BOTH pairs of opposite angles to be
?.
YES The same pairof opposite sides is parallel
and ?.
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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.
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Geometry--Ch. 6 Review
17) Given the following trapezoid and its
midsegment, find the value of x
(2x8) (8x5) 2 (6x3)
10x 13 12x 6
13 2x 6
By plugging the x 3.5back in, we can see
thatwere correct.
7 2x
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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 triangleis 180o, m?2
31o.
The two triangles in the kiteare ? (by SSS).
Therefore, weknow the other missing angles as
well.
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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