Download Final Review Ch 3 and 4

GEOMETRY
Final Exam Review – Chapters 3 and 4
Name: __________________
Period: _____
2. In the diagram below, 1  4 .
1. In the accompanying diagram, parallel lines l
and m are cut by a transversal t.
1
l
1
2
l
m
t
Which of the following must be true?
A. 1  2
B. 1 is the complement of 2 .
C. 1 is the supplement of 2 .
D. 1 and 2 are right angles.
3. Two angles of a triangle have measures of 55°
and 65°. Which of the following could not be a
measure of an exterior angle of the triangle?
A. 115°
C. 125°
3
4
m
2
t
Which of the following conclusions does not
have to be true?
A. 3 and 4 are supplementary angles.
B. Line l is parallel to line m
C. 1  3
D. 2  3
4. Solve for x.
(8x)º
B. 120°
D. 130°
(x -13)º
5. If m1   x  12  and m2   2 x  6  , find
each angle measure.
1
(3x + 25)º
6. Determine if the pair of triangles must be
congruent and if so by which property
l
2
2
m
t
m1  ______
m2  ______
b
2
4
yes, by ASA
yes, by SAS
yes by AAS
not necessarily congruent.
8. Give a congruence statement for two triangles
and name the theorem or postulate that proves the
congruence. Given; J  I ; IKH  JHK
7.
a
A.
B.
C.
D.
I
6
J
a
8
If m2  m8, then a // b because ____________
If m2  m6, then a // b because ____________
A.
B.
C.
D.
H
HJK  KIH , AAS
HJK  KIH , SAS
HJK  KIH , ASA
HJK  KIH , SSS
K
9. In the figure below, AC  DF and A  D .
10. In the figure below, AD P BC .
A
C
F
B
A
D
E
Which additional information would be enough to
prove that ΔABC  ΔDEF?
A. BC  EF
B. BC  DE
C. AB  DE
D. AB  BC
11. Determine if the pair of triangles must be congruent
and if so by which property
A.
B.
C.
D.
D
(3x-28)°
yes, by ASA
yes, by SAS
yes by AAS
not necessarily congruent.
13. Find the measure of the vertex angle of an
isosceles triangle if the measure of each base
angle is 34°.
15.Write a system of equations and solve for y and x.
B
(2x + 33)°
C
What is the value of x?
A. 37
B. 35
C. 61
D. 64
12. If pentagon BNRWG  pentagon PCMAT , then
A. BN  AT
B. WR  AM
C. WG  MT
D. GW  TM
14. Is ΔABC with vertices A (-1, 3), B (2, 1), and
C (1, 6) a right triangle? Justify your answer.
16. Solve for the variables in the rhombus below:
d2
56 a
2x - 4
y
x-3
3y+x
8d+9
b
c
e
17. Quadrilateral ABCD is a parallelogram. If
adjacent sides are congruent, which statement
must be true?
A.
B.
C.
D.
Quadrilateral ABCD is a square.
Quadrilateral ABCD is a rhombus.
Quadrilateral ABCD is a rectangle.
Quadrilateral ABCD is an isosceles
trapezoid
19. If two sides of a triangle are 6 and 15, what
are the possible lengths of the third side?
Between _____________ and _______________
18. Solve for x.
114°
x°
122°
137°
120°
93°
20. Is it possible to dtaw a triangle with sides of
length 4 cm, 6 cm, and 11 cm?
21. If the measure of one interior angle of a regular 22. Given the points A  3, 7  and B  2, 3 .find:
polygon is 135º, how many sides does it have?
a) The midpoint of AB
Show the algebraic set up and solution.
b) The slope of AB .
c)
23.
Find x.
24. The sum of the interior angles of a polygon is
the same as the sum of the exterior angles.
What type of polygon is it?
A. quadrilateral
B. hexagon
C. octagon
D decagon
(3x+50)°
(2x-10)°
100°
25. What values of x and y make quadrilateral
MNOP a parallelogram?
5y+9
N
The slope of the line perpendicular to AB
O
26. Given parallelogram MNPQ, solve
for x, y, and z.
x =________
M
144º
4x-11
y =________
21
M
26º
P
9y-19
27.
N
x
Given: AT bisects PTR
AT  PR ;
z = ________
y
P
z
Q
28. Given:
P
Prove: PAT  RAT
Prove:
EO bisects FC
FO // EC
F
FO  EC
A
R
O
R
T
E
C