Geometry Extended
FINAL - Review Packet
1) In CDE , mC  64 and mD  75 . What 2) The vertex angle in an isosceles triangle
measures 100. Find the measure of a base
is the shortest side of the triangle?
angle.
3) Given the statement ~ a  b
a) What is the converse?
b) What is the inverse?
c) What is the contrapositive?
4) If a triangle has two sides of length 8 and
12, what are the possible lengths of the third
side?
5) What is the measure of angle 1 and angle 2? 6) In right triangle ABC, mC  90 . How many
degrees are in A if the measure of exterior
ABD is 130?
A
C
B
D
7) Which three lengths could be lengths of the
sides of a triangle?
(12, 15, 27) (10, 15, 24) (9, 11, 22) (6, 7, 21)
8) The image of point (-2, 3) when
a) reflected in the x-axis:
b) reflected in the y-axis:
c) rotated 90°:
d) dilated by a factor of 2:
9) Find the value of x.
10) Which letter has line symmetry?
 3x  10  
 5 x  10  
11) Given that p is true and q is false, then
what is the truth value of
 p  q  q ?
13) If MN is an angle bisector, what is x?
R N T M S Q
12) In ABC , mA  65 and mB  45 .
What is the measure of the exterior angle at
C ?
14) In what quadrant on the Cartesian Plane is
the point (-3, -6)?
15) What is the midpoint of a segment with
the endpoints  3, 7  and  5,1 ?
16) a) By what method can
b) By what method can
17) Using Heron’s Formula,
Area  s  s  a  s  b  s  c  where s is half of
the perimeter, what is the area of the triangle,
to the nearest tenth?
10
12
ABX  DEY ?
ABC  DEF ?
18) a) ABC is a right triangle with the right
angle at C. What is the longest side of ABC ?
b) Given GHJ where GH  6 , JH  8 , and
GJ  9 . What is the smallest angle?
14
19) What is the measure of the vertex angle of
an isosceles triangle if one of the bases angles
measures 68?
20) What is the distance between the points
8, 2  and  4,5 ?
21) Given the line y  3x  5 ,
a) What is the slope of the line
perpendicular to the line?
22) Find the value of x. The diagram is not to
scale.
72°
b) What is the slope of the line parallel to
the line?
127°105°
x°
23) In XYZ , mX  30 and mY is five
times mZ . What is mZ ?
24) Given the points A  2, 7  and B  3,3 ,
25) What is the sum of the interior angles of an
18-gon?
27) What is the sum of the exterior angles of a
24-gon?
26) What is the measure of each interior angle
of a hexagon?
28) What is the measure of each exterior angle
of a decagon?
29) What is the number of sides of a polygon
where the sum of the interior angles is 540°?
30) What is the number of sides of a polygon
where each interior angle measures 135°?
what is the slope of AB ?
31) What is the number of sides of a polygon
where each exterior angle measures 40°?
32) What is the area of the figure?
33) In parallelogram ABCD, if mA  7 x 12
and mB  2x  3 , find mA
34) In parallelogram PQRS, if mSPR  30 ,
find mQRP
Q
R
A
D
30
°
P
B
S
C
35) In rectangle MNOP, if PX = 8, then MO =?
p
M
36) In rectangle ABCD, the diagonals are AC
and BD. If mABD  35 , find mACB .
B
A
35°
X
N
O
37) In rhombus EFGH, FG = 2x – 2 and
GH = x+8. Find x.
E
F
D
C
38) In rectangle ABCD, if BE = 2x + 3 and
CE = x + 6, find the value of x.
B
A
2x-2
E
H
G
x+8
39) In rhombus GHJK, diagonal HK is drawn
and mGHK  55 . Find mJ  ?
H
D
C
40) If the side of a square is 5, what is the
length of a diagonal?
J
55°
5
G
K
41) In parallelogram RSTU with diagonals RT
and SU interesecting at M, if RM = 4x + 3 and
MT = 5x - 2, find RT.
S
42) In a square, two sides have measures of
3x - 15 and 7x - 55. What is the measure of a
side of the square?
R
M
T
U
43) The angles of a quadrilateral are 4x + 25,
2x + 18, 80°, and 135°. Find x.
44) In trapezoid ABCD, mA  2x and
mD  8x  10 . Find x.
45) In isosceles trapezoid ABCD, AD = 3x + 5
and BC = 5x - 9. Find x.
46) In isosceles trapezoid ABCD, mB  2x 10
and mA  x  25 . Find x.
47) In trapezoid CDEF, CD = 7, EF = 15. What
is the length of median GH?
48) What is the area of the trapezoid?
8
D
C
6
G
H
E
14
F
49) If diagonal EG = 8 and diagonal FH = 12,
then find the area of the rhombus
E
50) In rhombus MNOP, mM  62 and
mMNP  x . Find x.
N
F
O
x
H
G
M
62°
P
51) What are the TWO properties of similar
polygons?
52) JKLM ~ PQRS,
What is x?
53) In a triangle, the sides are 8, 10, and 12.
In a similar triangle, the shorter side is 12.
What is the length of the longest side of the
second triangle?
54) In two similar triangles, the larger triangle’s
longest side is 24 and the corresponding side in
the smaller triangle is 10. If the perimeter of
the larger triangle is 60, what is the perimeter
of the smaller triangle?
55) In PNM , S is midpoint of PN and R is
midpoint of PM .
a) If NM = 46,
what is SR?
56) Given triangle ABC, with midpoints D, E,
and F. If DE = 8, EF = 9, and BC = 20, what is
the perimeter of triangle ABC?
B
b) If mN  47 ,
what is mPSR ?
D
A
E
F
57) If AC DE , find x
58) If AC DE , find x
59) If AC DE , find x
60) If AC DE , find x
C
61) In right triangle ABC, CD is an altitude.
Find x.
62) In right triangle ABC, CD is an altitude.
Find x.
10
20
x
63) In right triangle ABC, CD is an altitude.
Find x.
9
64) In right triangle ABC, CD is an altitude.
Find x.
3
65) Find the length of the missing sides.
66) Find the length of the missing sides.
67) Find the length of the missing sides.
68) Find the length of the missing sides.
69) Given points C and D, find distance CD
C (6, 2)
D (-4, -8)
70) Find the Midpoint of points C and D from
#69
71) Given a||b, find x.
72) In triangle EFG, FE  8 and FG  15 .
Which inequality best describes the measure of
EG?
A) 8  EG  15
B) 8  EG  15
C) 7  EG  23
D) 7  EG  23
73) By what method are the two triangles
congruent?
74) What is the slope of a line passing through
the points (1, -2) and (4, -7)?
75) Find x.
76) Find x.
77) Find x.
78) Find x.
79) Find x.
80) Find x.
58°
x
81) Find x.
82) Find x.
95°
x
65°
83) Find x.
84) Find x.
85) Find x.
86) Find x.
136°
87) Find x.
88) Find x.
89) Find x.
90) Find x.
x
24°
91) PQ = 40, AS = x, Find x.
92) Find x.
 x  2    y  5  36 ,
93) Given the equation
what are the center and the radius of the
circle?
2
2
 x  1   y  3
2
94) Graph the circle:
2
 16
95) Given a circle has a center of (2, -4) and
radius of 5, what is the equation of the circle?
96) What is the CENTER of a circle whose
diameter has the endpoints (4, 7) and (2, 1)?
97) Find the image of the point (-6, 2) under
R
the transformation 90 .
98) If M (2, 3) is the midpoint of AB and the
coordinates of A are (-3, 6), then find the
coordinates of B.
99) What is the volume of the rectanglur
prism?
100) What is the surface area of the rectanglur
prism?
101) What is the volume of the cylinder?
102) What is the surface area of the cylinder?
103) What is the volume of the triangular
prism?
104) What is the surface area of the cube?
105) What is the volume of the cone?
106) What is the lateral area of the cone?
107) What is the volume of the pyramid?
108) What is the volume of the sphere with a
radius of 3?
109) What is x?
110) a) Two sides of a triangle are 4 and 7.
The third side CANNOT measure:
11
7
5
4
b) Two sides of an isosceles triangle are 5 and
10. The length of the third side could be:
111) If the sides of a triangle measure 4, 9,
and 11, and the perimeter of a similar triangle
is 72, what is the measure of the longest side
of the similar triangle?
112) D and E are midpoints. Find AB.
113) Find x
114) In a right triangle, the hypotenuse
measures 15 and one leg measures 9.
What is the measure of the other leg?
115. Find the volume of the regular pentagonal prism.
116. Write all possible trig ratios for both non-right angles in your special right triangles.
30-60-90
45-45-90
117.
Name Special Angle Pairs and Describe their relationships.
Angle Puzzles. Find all #’ed angles in the picture below.
Fina all possible angles in picture below