Download Geometry 300 Midterm

GEOMETRY HONORS MIDTERM REVIEW #1
Part I - Answer all questions in this part. Each correct answer will receive 2 credits.
No partial credit will be allowed.
1. In the diagram of ABC and DEF below, AB  DE, A  D, and B  E.
Which method can be used to prove ABC  DEF?
(1) AAS
(2) SAS
(3) ASA
(4) HL
2. In a pentagon, what is the difference between the sum of the exterior angles and
the sum of the interior angles?
(1) 180°
(2) 120°
(3) 90°
(4) 60°
3. In the accompanying diagram, transversal MN intersects parallel lines RS and TU at
P and Q respectively. If mRPM  50 , find mPQU .
M
R
S
P
T
U
Q
N
(1) 50°
(2) 130°
(3) 40°
(4) 100°
4. In ABC, mA  95 , mB  50 , and mC  35 .
relates the lengths of the sides of this triangle?
(1) AB < BC < CA
(2) AB < AC < BC
Which expression correctly
(3) AC < BC < AB
(4) BC < AC < AB
5. What is the converse of the statement, “If I do well on this test, then I am happy.”?
(1) If I do well on this test, then I am not happy.
(2) If I do not do well on this test, then I am happy.
(3) If I am not happy, then I do not do well on this test.
(4) If I am happy, then I do well on this test.
6. A polygon is transformed according to the rule: (x,y)  (x  2,y) . Every point of the
polygon moves two units in which direction?
(1) up
(2) down
(3) left
(4) right
7. Side PQ of PQR is extended through Q to point T. Which statement is not always
true?
(1) mRQT  mR
(2) mRQT  mP
(3) mRQT  mP  mR
(4) mRQT  mPQR
8. If the measures of two complementary angles are in the ratio of 1:5, what is the
measure of the larger angle?
(1) 72°
(2) 75°
(3) 144°
(4) 150°
9. If Mary gets an A in math and an A in science, then she is happy. Mary is not happy,
but she got an A in math. What is a logical conclusion?
(1) Mary got an A in science.
(2) Mary did not get an A in either math or science.
(3) Mary got an A in both math and science.
(4) Mary did not get an A in science.
10. In the diagram of ABC below, AB  AC . The measure of B  64 .
What is the measure of A ?
(1) 37°
(2) 58°
(3) 52°
(4) 86°
11. In the diagram of trapezoid ABCD below, diagonals AC and BD intersect at E and
CD  BA . Which statement must be true based on the given information?
(1) AC  BD
(2) CD  AD
(3) CDE  BAD
(4) BC  AD
12. In the diagram below of parallelogram ABCD with diagonals AC and BD,
m1 52 and mDCB  105 . What is the measure of 2?
(1) 65°
(2) 23°
(3) 48°
(4) 56°
13. What is the slope of the line containing the points (3,4) and (-6,10)?
(1)
1
2
(2) 2
2
3
3
(4)
2
(3)
14. Which image represents a line reflection?
15. Line segment AB has endpoints A(2, 3) and B(4,6) . What are the coordinates of
the midpoint of AB?
(1) (-2,3)
1
(2) (1,1 )
2
(3) (1,3)
1
(4) (3,4 )
2
16. Which statement is expressed as a biconditional?
(1)
(2)
(3)
(4)
Two angles are congruent if they have the same measure.
If two angles are both right angles, then they are congruent.
Two angles are congruent if and only if they have the same measure.
If two angles are congruent, then they are both right angles.
17. The endpoints of AB are A(4,2) and B(8,-2). If A"B " is the result of the
transformation of AB under a D 1 R90 what are the coordinates of A " and B"?
2
(1) A"(2,10) and B "(6,8)
(2) A"(1,2) and B"(14
, )
(3) A"(2,7) and B "(10,5)
(4) A"(14, 2) and B"(22, 4)
18. What is the measure of an interior angle of a regular octagon?
(1) 45º
(2) 60º
(3) 120º
(4) 135º
19. A parallelogram must be a rectangle if its diagonals
(1) are congruent
(2) bisect each other
(3) are perpendicular to each other
(4) bisect the angles through which they pass
20. The length of the side of a square is 5. What is the length of the diagonal in
simplest radical form?
(1) 5 5
(3)
50
(2) 5 2
(4) 25
GEOMETRY HONORS MIDTERM REVIEW #2
1. As shown in the accompanying diagram, a rectangular gate has two diagonal
supports. If m1 = 42º, what is m2?
2. Given: Two is an even integer or seventeen is an even integer. Determine the truth
value of this disjunction. Justify your answer.
3. Can the measures 3 inches, 3 inches and 6 inches form an Isosceles Triangle? Justify
your answer.
4. Write a statement that is logically equivalent to the statement “If two triangles are
congruent, then all three pairs of corresponding sides are congruent.” Identify the
new statement as the converse, inverse, or contrapositive of the original statement.
5. In the diagram below of isosceles trapezoid DEFG, DE GF , GD  2x  y ,
EF  7y  2x , and x = 3. Find the value of GD.
D
2x + y
G
E
7y - 2x
F
6. The degree measures of the angles of  ABC are represented by x, 3x and 5x — 54.
Find the measure of the largest angle of the triangle.
7. The coordinates of the vertices of parallelogram ABCD are A(-2,2), B(3,5), C(4,2),
and D(-1,-1).
a) Graph and state the coordinates of the vertices of parallelogram A”B”C”D” that
result from the transformation ry axis T0,3 .
b) Name the transformation that maps parallelogram ABCD to A”B”C”D”?
c) Indicate if the above transformation is an isometry. Justify your answer.
8. Triangle ABC has coordinates A(-6,2), B(-3,6), and C(5,0). Find the perimeter of the
triangle. Express your answer in simplest radical form. [The use of the grid below is
optional.]
9. In the diagram below of ABC with side AC extended through D, mA  x  4 ,
mBCD  3x , and mB  48 . Which side of  ABC is the longest? Justify your answer.
B
A
C
D
GEOMETRY HONORS MIDTERM REVIEW #3
1. Complete a formal proof.
BD
(A  B)  C
C
A
___________
D
2. The vertices of quadrilateral ABCD are A(-2,-1), B(2,-4),C(2,1), D(-2,4). Prove that
ABCD is a rhombus.