Download n – 2

1a)
Yes, it has all straight sides and
is a closed figure.
4 sides = quadrilateral
1b)
Irregular because even though all
sides are congruent, NOT all
angles are congruent!
Convex (because no corners are
caved in).
2a)
No, not a polygon because it
has curves.
N/A (don’t need to answer the
second part)
3)
Sum of interior angles = (n – 2)180
Octagon: (8 – 2)180 = 1080°
Each angle means: 1080 ÷ 8 =
135°
Each exterior angle = 360/n
360 / 8 = 45°
4)
Sum of interior angles = (n – 2)180
Hexagon: (6 – 2)180 = 720°
(It only wants “sum” this time !)
5)
Sum of interior angles = (n – 2)180
Pentagon: (5 – 2)180 = 540°
Each angle means: 540 ÷ 5 =
108°
Each exterior angle = 360/n
360 / 5 = 72°
M
N
5x+14
P
6x
O
6a)
In a parallelogram, opposite
sides are congruent.
5x + 14 = 6x
x = 14
(Solve for x)
Plug back into MP: 5(14)+14 =
84
M
N
5x+14
P
6x
O
6b)
In a RHOMBUS, all 4 sides
are congruent.
So, MP=MN ; MN = 84
Z
7.
Y
W = (7,1)
X
Use
same
slopes
to find
W.
M
16x+18
22x
P
O
N
8a)
In a rhombus, all 4 sides are
congruent.
22x = 16x +18
6x = 18
x=3
(Solve for x)
8b)
Plug back into RT: 22(3) = 66
RS = RT = 66
8c)
It’s a rhombus, so TU=SU=RT=RS
So, TU = SU = 66
8d)
Perimeter = all 4 sides added up
66 + 66 + 66 + 66 = 264
9a)
Inside a kite, you have 4 right
triangles. All angles of a
triangle add up to 180°
9x + 11 + x +4 + 90 = 180
10x + 105 = 180
10x = 75
x = 7.5
9b)
Plug “x” back into angle BDC
9(7.5) + 11 = 78.5°
9c)
Plug “x” back into angle DCA
(7.5) + 4 = 11.5°
C
B
Y
A
D
10a)
In an isosceles trapezoid, diagonals
are congruent.
So, BD = AC
BY = CY
AY = DY = 15
BY = BD – DY = 22.4 – 15 = 7.4
10b)
In an isosceles trapezoid,
diagonals are congruent.
BY = CY = 7.4
10c)
In an isosceles trapezoid,
diagonals are congruent.
AY = DY = 15
11a)
In a parallelogram, opposite angles
are congruent AND consecutive
angles are supplementary.
So, R + T = 180
5x – 30 + 2x = 180
7x – 30 = 180
7x = 210
x = 30
11b)
Plug “x” back into angle T
2(30) = 60°
11c)
Plug “x” back into angle R
5(30) – 30 = 120°
11d)
Since opposite angles are congruent,
Angle T = Angle S = 60°
11e)
Angle S changes from acute to
OBTUSE.
12)
Since the two shorter sides are
congruent and the two longer sides
are congruent (use distance formula
or pyth thm), this is a KITE.
13)
Sum of interior angles = (n – 2)180
Hexagon: (6 – 2)180 = 720°
Each angle means: 720 ÷ 6 =
120°
14)
For a square, all sides are the same length.
So, since perimeter =36
Each side = 36 ÷ 4 = 9
Diagonal is the hypotenuse of a right triangle.
Use Pythagorean Theorem:
a2 + b2 = c2
92 + 92 = c2
81 + 81 = c2
Which simplifies to 9√2
162 = c2
15)
Sum of interior angles = (n – 2)180
Pentagon: (5 – 2)180 = 540°
Adding up all the angles = 540°
90 + 90 + 90 + x + x = 540°
270 + 2x = 540
2x = 270
→ x = 135
16)
Sum of interior angles = (n – 2)180
Quadrilateral: (4 – 2)180 = 360°
Adding up all the angles = 360°
80 + 70 + 150 + angle C = 360
300 + angle C = 360
Angle C = 60°
17)
Inside a kite, you have 4 right
triangles. Find the area of all the
triangles to get the total area of the
kite.
A=½bh
For small triangles: A = ½ (6)(8) =
24
For big triangles: A = ½ (8)(15) = 60
Total area = 24 + 24 + 60 + 60 = 168
18)
Each exterior angle = 360/n
360 / 8 =
45°
19)
Sum of interior angles = (n – 2)180
Decagon: (10 – 2)180 = 1440°
Each angle means: 1440 ÷ 10 =
144°
20)
Look at checklist:
For a rectangle only choice A is
always true:
Diagonals are congruent
21)
Look at checklist:
All squares are rhombi because
they have 4 congruent sides and
bisecting diagonals.
22.
Sum of interior angles = (n – 2)180
Quadrilateral: (4 – 2)180 = 360°
Adding up all the angles = 360°
2x – 5 + 3x + 80 + x + 15 = 360
6x + 90 = 360
6x = 270
x = 45
23)
In a parallelogram, opposite angles
are congruent AND consecutive
angles are supplementary.
So, E + H = 180 (since they are
supplementary , same-side interior)
E + 35 = 180
Angle E = 145°
24.
Think of splitting the regular hexagon up into
triangles. Each triangle in this case is
EQUILATERAL.
5”
5”
5”
In a regular hexagon, all sides are
congruent, so perimeter = 5 + 5 + 5 + 5 +
5 + 5 = 30
H (6,11)
25.
I (8,7)
G (2,5)
J = (-8,-5)
25a.
Use midpoint formula (on formula
sheet)
H (6, 11)
x1,y1
I (8, 7)
x2,y2
W = 6 + 8 , 11 + 7 = (7, 9)
2
2
25a.
Use midpoint formula (on formula
sheet)
G (-2, 5)
x1,y1
J (-8, -5)
x2,y2
Z = -2 + (- 8) , 5 + (-5) = (-5, 0)
2
2
H (6,11)
25.
W (7,9)
I (8,7)
G (2,5)
Z (-5,0)
J = (-8,-5)
Use
same
slopes
to find
W.
25b.
Use slope formula (on formula sheet)
G (-2, 5)
x1,y1
H (6, 11)
x2,y2
m = 11 – 5 = 6
6 – (-2)
= 3 (slope of GH)
8
4
25b.
Use slope formula (on formula sheet)
I (8, 7)
x1,y1
J (-8, -5)
x2,y2
m = -5 – 7
-8 – 8
= -12
-16
= 3 (slope of IJ)
4
25b.
Use slope formula (on formula sheet)
W (7, 9)
x1,y1
Z (-5, 0)
x2,y2
m=0–9
-5 – 7
= - 9 = 3 (slope of WZ)
-12
4
25b.
Conclusion: All 3 segments of the
trapezoid are PARALLEL since they
all have the same slopes.
25c.
Find distance using Pythagorean theorem or
distance formula (on formula sheet)
G (-2, 5)
x1,y1
82 + 62 = c2
64 + 36 = c2
100 = c2
H (6, 11)
x2,y2
GH = 10
25c.
Find distance using Pythagorean theorem or
distance formula (on formula sheet)
I (8, 7)
x1,y1
J (-8, -5)
x2,y2
162 + 122 = c2
256 + 144 = c2
400 = c2
IJ = 20
25c.
Find distance using Pythagorean theorem or
distance formula (on formula sheet)
W (7, 9)
x1,y1
Z (-5, 0)
x2,y2
122 + 92 = c2
144 + 81 = c2
225 = c2
WZ = 15
25d.
Conclusions:
The median is parallel to the two
bases.
The median is the average of the two
parallel bases: 10 + 20 = 15
2