Download Geometry Midterm Review Chapters 1

Geometry Midterm Review
Chapters 1-4
For 1-12, justify each statement with a Geometry Rule
D
1. m∠AXB = m∠EXF
C
2. AX + XE = AE
E
3. m∠BXE + m∠EXF = 180°
4. If BF ⊥ DX, then ∠BXD ≅ ∠DXF
F
B
X
5. If X is the midpoint of BF, then BX = XF.
A
6. If BF ⊥ DX, then ∠DXE and ∠EXF are complementary.
If XC bisects ∠BXD, then
7.
1
m∠BXC = m∠BXD.
2
8. m∠AXB + m∠BXC = m∠AXC.
9.
10.
11.
If ∠BXC and ∠CXD are complementary, then
m∠BXC + m∠CXD = 90°
If BF ⊥ DX, then ∠BXD is a right angle
If ∠BXC and ∠CXF are supplementary,
then m∠BXC + m∠CXF = 180°
12. If X is the midpoint of AE ,
then AX = ½ AE
For #13, write an equation and solve for the angles.
13. The sum of an angle’s complement and twice its supplement is 324°. Find the angle, its
complement, and its supplement.
For #14 give a one-word response that best describes the answer:
14.(a) the supplement of an acute angle is ______________
(b) the complement of an acute angle _____________
(c) the supplement of an obtuse angle is ______________
(d) the supplement of a right angle is ____________
For #15-16, refer to the diagrams and solve for all unknowns.
15. Solve for x, m∠ABC, m∠DBE
16. Solve for x, m∠FGH, m∠HGI
A
H
D
4x - 27
B
3 + 2x
8x - 40
C
E
F
2x + 20
I
G
For #17, refer to the diagram to complete the question:
17. (a) Name a straight angle
W
O
3
(b) Name two adjacent angles.
2
Z
1
(c) Name an acute angle.
X
(d) Give another name for angle 2.
(f) What two angles add together to create
∠XOZ ?
(e) Give another name for WO
For #18, complete the proof:
18. Given:
BA = CA
BX = CY
A
Prove: XA = YA
X
Y
C
B
1.
1.
2.
BA = BX + XA
CA = CY + YA
3.
4.
5.
Given
2.
3.
BX = CY
Y
Substitution
4.
5.
For 19-21, complete with always, sometimes, or never.
19. Alternate interior angles are _____________ congruent.
20. Vertical angles are __________ congruent.
21. Corresponding angles are ___________ congruent.
For 22-24, refer to the diagram:
22. Name two pairs of alternate interior angles
23. Name three pairs of corresponding angles
1
4
2
5
8
3
6
7
24. Name two pairs of same-side interior angles
For #25, complete the proof:
25. Given: ∠2 ≅ ∠6
Prove: l & m
1
2
4 3
l
6
5
1.
2.
3.
4.
Statements
________ ∠2 ≅ ∠6 ___________
_________ ∠2 ≅ ∠4 __________
___________________________
___________________________
m
7
8
Reasons
1.
Given___________
2. __________________________
3. __________________________
4. __________________________
For #26-27, classify the triangles based on their sides and angles.
27. The perimeter of + ABC is 36. Is the
26.
triangle equilateral, isosceles, or scalene?
8x - 20
B
3x + 1
2x + 2
3x + 5
2x
A
For #28, l & m . Write two equations and
solve for x and y.
4x - 3
C
For #29, find the following:
29. (a) each exterior angle of a hexagon
28.
(b) each interior angle of a pentagon
2x + 40
(c) sum of the interior angles of an octagon
5y + 20
x + 80
(d) each interior angle of a decagon
For #30-32, name a triangle congruence and the postulate you would use to show that the
triangles are congruent.
F is the midpoint of EH
30.
31. JM ⊥ LK , LJ ≅ KJ
32.
ED & HG
B
J
E
G
A
60
61
F
59
60
D
H
L
M
K
M
For #33-34, complete each proof:
N
B
33.
Given: CD bisects ∠BCJ and ∠BDJ
C
3
2
1
4
D
Prove: BD ≅ JD
J
1.__________________________
1.__________________________
2.__________________________
2.__________________________
__________________________
3.__________________________
3.__________________________
4.__________________________
4.__________________________
5.__________________________
5.__________________________
34. Given: WX & ZY , WY & ZX
W
X
3
Prove: WX ≅ ZY
1
Y
2
4
Z
1.__________________________
1.__________________________
2.__________________________
2.__________________________
__________________________
3.__________________________
3.__________________________
4.__________________________
4.__________________________
5. _________________________
5. __________________________
35. List three examples of undefined terms: _________, __________, __________
36. List three examples of defined terms: _________, __________, __________
37. Which of the following describes deductive reasoning:
A.
B.
C.
D.
E.
using logic to draw conclusions based on accepted statements
accepting the meaning of a term or definition
defining mathematical terms to correspond with physical objects
inferring a general truth by examining a number of specific examples or pattern
none of the above
38. Which of the following describes inductive reasoning:
A.
B.
C.
D.
E.
using logic to draw conclusions based on accepted statements
accepting the meaning of a term or definition
defining mathematical terms to correspond with physical objects
inferring a general truth by examining a number of specific examples or pattern
none of the above
A
B
2
1
F
10
11 8
7
E
9
5
3
39. If ∠9 ≅ ∠5 , name a pair of segments
that must be parallel: ______________
4 C
6
D
40. If AB & FC , name a pair of angles
that must be congruent: ______________