Download Study Guide for Final Ch 1-6

GEOMETRY
STUDY GUIDE FOR FALL SEMESTER FINAL
CHAPTERS 1 - 7
Indicate the best answer by writing the appropriate letter.
1. If M is between R and T then ___?___.
A) MR + RT = MT
B) RM = MT
C) RM + MT = RT
2. The two angles in a pair of vertical angles are always __?__.
A) congruent
B) adjacent
C) acute
D) MR = RT
D)  and acute
3. If two angles are complementary to the same angle, then they are __?__ to each other.
A) complementary B) vertical
C) adjacent
D) congruent
4. In a plane, two lines perpendicular to the same line are __?__ parallel.
A) always
B) sometimes
C) never
5. Two lines parallel to the same plane are __?__ parallel to each other.
A) always
B) sometimes
C) never
6. Which of the following is the hypothesis of the conditional: I’ll stay if I win.
A) I’ll stay.
B) I win.
C) I’ll leave if I lose D) I’ll win if I stay.
7. Choose the statements that must be true for a rhombus.
I. The diagonals are congruent .
II. The diagonals bisect each other.
III. The diagonals are perpendicular.
IV. The diagonals bisect the angles.
8. Choose the statement that must be true for a rectangle.
I. The diagonals are congruent .
II. The diagonals bisect each other.
III. The diagonals are perpendicular.
IV. The diagonals bisect the angles.
9. If CAT  DOG, then which of the following are true?
I. A  O
II. AT = DO
III. TC = GD
IV. CTA  DGO
r
1
4
Use for problems
#10 - 12
10. If r || s, then 1  __?__.
A) 9
B) 11
C) 5
D) 9 and 5
11. If 3  12, then __?__.
A) b || c
B) r || s
12. If b || c, then 6 must be __?__ to 3
A) congruent
B) supplementary
5
7
s
3
6
11
13
8
C) b || c and r || s
9
2
16
10
12
14
b
c
15
D) none of these
C) congruent and
supplementary
D) adjacent
13. If two angles of a triangle measure 47 and 93, then the measure of the third angle is __?__.
14. The measures of the angles in a triangle are in the extended ratio 2: 4: 9. Find the measure of the
largest angle.
15. The diagonals of a trapezoid __?__ bisect each other.
A) always
B) sometimes
C) never
16. If the lengths of two sides of a triangle are 7 and 13, then the length of the third side must be
between _?_ and _?_.
17. In ABC, mA = 4x + 5, mB = 2x + 20, and mC = 5x – 10. The two congruent sides of the
triangle are __?__.
A) AB and AC
B) AB and BC
C) AC and BC
D) AB , BC , and AC
18. If ABCD is a parallelogram, then which of the following must be true?
A) A  D
B) AB  DA
C) AB  BC
D) mB+ mC = 180
19. A and B are supplementary, mA = 2n, and mB = 3n + 20. Find mB.
1 2
20. Given: a || b, m1 = 3x + 30; m3 = 2x. Find m4.
3
5
21. Which of the following is a false statement?
A) Points A, B, and C are coplanar.
B) Planes M and N intersect in DE
C) Exactly one line contains points B and C.
D) Exactly one plane contains point B and DE
a
Use for
question #20.
b
4
M
A
D
E
N

C
B
22. RING is a parallelogram. RI = x + 6, IN = 2x + 4, and NG = 3x. Find GR.
R
G
I
N
23. Which of the following could not be the lengths of the sides of a triangle?
A) 1, 3, 2
B) 2.5, 5, 3
C) 4, 4, 4
D) 2, 3, 2
24. Which of the following is the converse of the statement:
If A and B are right angles, then A  B?
A)
B)
C)
D)
If A and B are not right angles, then A  B.
If A  B, then A and B are not right angles.
If A and B are not right angles, then A  B
If A  B then A and B are right angles.
25. What is the sum of the measures of the interior angles of a convex hexagon?
26. A regular polygon has 12 sides. What is the measure of each interior angle?
27. If RA = x and AK = 4x + 6, find the coordinate of the midpoint of AK .
A
R
K
4
12
B
28. BD bisects ABC. mABD  4x  4 and mCBD  5x  1.
Find the value of x.
A
D
29. Find the value of y.
(6x – 20)
(4y + 8)
(3x + 10)
C
30. Through a point not on a line, how many lines are parallel to the given line?
31. If XY || WZ , which pair of angles are congruent?
Y
A) 2  5
B) 3  6
C) 2  6
1
D) 8  4
8
X
32. Find x.
3
2
7
6
5
x
24
108
33. The median of a trapezoid measures 23 cm and one of the bases is 15 cm. Find another base.
34. Draw three types of lines in the space provided.
A
B
35. Complete the proof.
Given: OA bisects BOF and
Prove: mAOF = mEOF.
O
OB bisects AOC.
F
C
D
E
Conclusions
1. OA bisects BOF and BD bisects AOC
2. mBOA = mAOF
mBOC= mBOA
3. mBOC = mAOF
4. mEOF = mBOC
5. mAOF = mEOF
Justifications
1. Given
2. ?
3. ?
4. ?
5. ?
W
Z
4