Download Algebra 1 A - Parkway C-2

Geometry A 1st Sem. Final Review Worksheet
Name _______________________
In Exercises 1–8, use the diagram.
1.
2.
3.
4.
5.
6.
7.
8.
Give two other names for EF
Give another name for plane A.
Name three points that are collinear.
Name four points that are coplanar.
Give another name for EF
Name a ray with endpoint E that is an opposite ray of EC
Name a point that is not coplanar with points C, E, and B.
Name a ray with endpoint F.
9. Write the equation of the bisector of segment NO with N(2, -4) and O(8,2) that goes through P(-5, -6).
10. Find the coordinates of the midpoint of the segment with endpoints G(-6,7) and H(10, -2)
11. Find the coordinates of the other endpoint of a segment with given endpoint Q(2,-3) and midpoint M(-6,-4).
12. Tell whether the statement is always, sometimes, or never true. Explain your reasoning.
A pair of opposite rays form a straight angle.
The measures of two acute angles add up to 90°.
If C is in the interior of ADB, then ADC  CDB.
When a ray bisects a straight angle, two congruent acute angles are formed.
Can the statement be assumed to be true from the diagram? Explain.
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17.
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23.
AB and AD are opposite rays.
BAC and CAD are supplementary.
BAC  BAE
CE  plane S
BD lies in plane S and in plane T
If G is a point in plane S, then CG lies in S.
CE bisects BD
Plane T bisects BD .
24. Write the converse of each true statement. If the converse is also true, combine the statements to write
a true biconditional statement.
If an angle measures 30°, then it is acute.
If two angles are supplementary, then their sum is 180°.
If an animal is a panther, then it lives in the forest.
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28. Given m<ABC = 94o,
find m<BDC.
35.
2
Use the diagram at the right to find two examples of:
*appear to be*
36. skew lines
37. parallel lines
38. parallel planes
39. Write the equation of a line parallel to y  3 x  2 that goes through the point (0, -3).
40. Write the equation of a line perpendicular to the line y 
point (-4, 2)
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x  7 that goes through the
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41. Find the distance between the following lines: y  3 x  6 and y  3 x  4
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9. Solve for x and y
1. Find the values of x and y.
2. Use the given coordinates to determine if ABC  DEF.
A(1, 1), B(4, 0), C(7, 5),
D(4, –5), E(6, –6), F(9, –1)
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1. Circle T if the statement is true. Circle F if the statement is false.
A. If a triangle is equiangular, then it is equilateral.
B. If a triangle is equiangular, then it is isosceles.
T
T
F
F
C. If two triangles are equilateral, then they are congruent.
T
F
D. In Δ ABC, if AC = AB, then A  B .
T
F
E. AB and DC intersect at point P, AP  CP and BP  DP .
T
F
F. If AB = SR, AC = TR, and A  R , then ABC  RST .
T
F
G. If AG = BH, AK = BP, and G  H , then AGK  BHP .
T
F
H. If MKT  NBR , then T  R , MK = BN, and KT = BR.
T
F
I. Two triangles are congruent if the three angles of one triangle are
congruent to the three angles of the other triangle.
T
F
J. Two triangles are congruent if two sides and an angle of one
triangle are congruent to two sides and an angle of the other.
T
F
17. The angles of a triangle follow the ratio 4:5:11. What are the measures of the angles?
26. Find each missing length.
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Find mR .
O
138°
M
In the diagrams, MOUS ~ TRAP.
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Find mP .
42°
S
U
y
R
T
Find the value of x.
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Find the value of y.
x
8
P
Find the length of the segment determined by the points given below.
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2.
(2.5, 7.8) and (-5.4, 13.7)
Find the midpoints of each of the segments determined by the given points.
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6.
(134, -93) and (-23, 121)
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A
Determine if the given lines are parallel, perpendicular, or neither.
y  6( x  1)  3
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2.
3.
7.
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y  x 9
8.
2
9 x  6 y  36
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y   x  10
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9.
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y  ( x  12)  19
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x9
x4
12 x  2 y  6
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x  2 the bisector of the segment?
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A perpendicular bisector?
9. Is the line y 
10. Is the line y  5 x  2 the bisector of the segment with endpoints P (-14, 10) and U (10, 6)? A perpendicular
bisector?
15. Write the equation of the bisector of segment YA with Y (-1, 21) and I (-9, 19) if the bisector also goes
through the point (7, 7).
14. Write the equation of the bisector of segment GO with G (-10, 2) and O (14, 19) if the bisector also goes
through the point (2, 4).
16. Write the equation of the perpendicular bisector of segment OH with O (9, 3) and H (-12, 10).
18. Write the equation of the perpendicular bisector of segment BK with B (5, 4) and K (9, 4).
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For #2-7, please use the coordinate plane to the right.
2. Write the equation of the line through
points S and E
3. Are points S, R, and T collinear?
How do you know?
4. What is the midpoint of BP ?
5. Find the other endpoint of the segment
with endpoint E and midpoint M.
6. Would the lines through point S and E be parallel
to the line through R and M. How do you know?
7. Find the distance between points Q and P
9. Find the distance between AH and TC .
10. Find the distance between Point W and TC .
4. Determine if ΔFLO and ΔWER are similar. Justify your answer.
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Geometry A
Finals Proof Practice
1.
2.
Name ___________________________
Given:
m1  m2
Prove:
4 and 5 are supplementary.
Given:
 || m
1 and 2 are supplementary.
a || b
Prove:
a
3.
4.
5.
6.
Given: CDE  A and l  AB .
Prove:
l  DE
Given:
DC bisects ADE ; 6  8
Prove:
AB CD
Given:
BC EF ; 6  7
Prove
EA CD
Given : m3  m6  180
m2  m3  180
Prove
BC EF
10
2
3
1

m
b
7.
Given:
Prove:
L
LGO is isosceles with base LO .
GA bisects OGL .
OGA  LGA
A
G
O
S
8.
Given:
Prove:
9.
MI bisects I .
IM bisects M .
MIS  MIT
I
M
T
Given: GJ  KI and KH  GI
Prove: HKI ~ JGI
A
10.
Given:
Prove:
ABC  DEC
CB  CE
CBA  CED
E
C
B
D
11.
Given:
Prove:
Diagram
GHI  JKL
12.
Given: E is the midpoint of
B
A
13. Given: AB || DC
both AC and BD
E
Prove:
ABE  CDE
Prove:
D
14.
C
GIVEN: Diagram
PROVE: ACD ~ EGH
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ABE ~ CDE