Geom 1-2 (E)
Final Exam Study Guide – Fall 2015
Name: ____________________________________
Period: ____
1. Using the diagram to the right, name all angles that can be called K . (6 total!)
2. Briefly explain the difference between ray GH and ray HG.
Use the diagram at the right to answer #4-8
3. AG
GN 
4. AG
AT
5. NO
NP 
6. PN
GT 
GT 
Use the diagram of the rectangle ABDE (All right angles) to answer questions 7-9.
7. If
mABE  47 , what is mEBC ?
8. If
mCDE  54 , what is mEDA ?
9. If
mAEB  85 what is mBEC ?
Triangle inequality Theorem.
10. Can the following three segments make a triangle: 5,7,12 Why or why not?
11. If two sides of a triangle measure 2.5 units and 3.8 units, what is the largest the third side could be?
12. If two sides of a triangle measure 2.5 units and 3.8 units, what is the smallest the third side be?
13. Using your answers from above, if two sides of a triangle measure 12 and 16, what are the restrictions on the length of the third
side of the triangle? Write your answer as a compound inequality.
Using the diagram at the right, state whether there is betweenness for the given points.
14. Is G between E and T?
15. Is O between E and N?
Angle measurements with algebra
16. Given: XYZ is a right angle
m1   3x  4 
m2   x  6 
Find: x and m1 .
m1  55.7
m2  90.4
Find: m3
17. Given:
18. Given:
GB bisects AGC
mAGB  7 x  22
mBGC  2x  7
a.) Draw this picture.
b.) Find the value of x .
c.) Find mAGC .
19. Given: QA and QR trisect UQK
mUQR  2 x  5
mAQU  4 y  6
mRQK  46
a.) Draw this picture.
b.) Find the value of x .
c.) Find the value of y .
mFGH  8x  2
mABD  3x 11
FGH and ABD are complementary.
Find: mABD
20. Given:
mFGH  2x  7
mABD  5x  4
FGH and ABD are supplementary.
Find: mFGH
21. Given:
22. Write the converse, the inverse, and the contrapositive of the following conditional. State whether each is true or false.
Conditional:
If an angle is 125°, then it is obtuse.
Converse: ___________________________________________________________________________________________________
Inverse: _____________________________________________________________________________________________________
Contrapositive: _______________________________________________________________________________________________
23. List both conclusions that can be drawn using all 3 of the conditional statements below
p ~ q
r ~ w
~rq
24. Given: 1 and 2 are supplementary
3 and 2 are supplementary
Conclusion:
Reason:
25. Given: PQR is supplementary to QRS
QRS is supplementary to TWX
mPQR   5x  48 
mTWX   2 x  30 
Find : mQRS
26. The measure of an angle is forty less than the supplement of the angle. Find the measure of the angle.
27. The supplement of an angle is 10 more than 2 times the measure of the complement of the angle. Find the measure of the
complement.
28.) If the perimeter of ABC is 44 units, is triangle
the value or values of x and the lengths of all 3 sides.
ABC scalene, isosceles, or equilateral? Justify your answer by finding
Variable
x
= _____
Side Lengths
AB
AC
BC
= _____
= _____
= _____
29.) Find the missing values for x and y.
x = _______
y = _______
30.) Find the missing values for x, y, and z.
x = _______
y = _______
z = _______
31. Given: 4 is complementary to
m1  128 .
8
Find all the other angle measures.
True and False.
32. _______________ If two complementary angles are congruent, then each is a right angle
33. _______________ If mP = 100°, then P has no complement
34. _______________ It is possible for two lines to intersect in such a way that three of the angles formed have measures
of 20 , 70 , and 20 .
35. _______________ If two angles are complementary then they are both acute.
Complete the following statements
36. If triangle ABC is isosceles with a base of AC, and angle B measures 40 degrees, what is the measure of angle A?
37. If
XYZ is equilateral, X has a measure of 4a , Y has a measure of 3b , what is the value of a  b ?
38. If a segment is drawn from the vertex of one angle in a triangle and is perpendicular to the opposite side, then it is called a(n)
________________.
39. If a segment is drawn from the vertex of one angle in a triangle to the midpoint of the other side, then it is called a(n)
____________________.
40.
DOG has side measurements of: DO  7 OG  10 DG  9 . Which angle is largest? Briefly explain.
41.
CAT has angle measurements of: C  50 A  60 T  70 . Which side is smallest? Briefly explain.
42. BD is the median to
AC with AD  4x  5 and AC  10x  30 . Find the measure of DC .
43. Find the value of x in the diagram below.
44. Solve for
x and y .
45. If a || b , find
m1.
46. Find all missing angle measures.
You may write your answers in
the picture
47. State which lines are parallel and why if given the following:
a.) 2  14
b.)
12  13
c.)
6 is supplementary to 11
48. In each drawing below, state name the congruent triangles and the postulate used (SSS, SAS, ASA, AAS, or HL).
Proofs. You will not have enough room to complete these proofs on this paper. Please use a separate sheet and attach it when done.
49. Given:
Prove:
50.
51.
KS  AK
AR  AK
SKP  RAP
PKA is isosceles
52. Given: C is a midpoint of BD
 D and  B are right angles
Prove: AB  DE
53.
(Hint: You can add extra segments)
54.
AC
BD is an altitude of ABC
Prove: ABC is isosceles
55. Given: D is the midpoint of