Download Chapter 4 Review – Geometry 4.1, 4.2, 4.3, 4.4, 4.5, 4.6

Name: ______________________________________________ Date: ___________________ Period: _______
Chapter 4 Review – Geometry
4.1, 4.2, 4.3, 4.4, 4.5, 4.6, 4.7, 4.8, 5.5, 5.6
Matching
_______ 1. isosceles triangle
A. triangle with all angles congruent
_______ 2. equiangular triangle
B. triangle with no congruent sides
_______ 3. scalene triangle
C. triangle with one right angle
_______ 4. right triangle
D. angle formed by extending side of ∆
_______ 5. equilateral triangle
E. triangle with all sides congruent
_______ 6. obtuse triangle
F. triangle with all angles less than 90
_______ 7. acute triangle
G. triangle with one angle greater than 90
_______ 8. exterior angle of ∆
H. triangle with at least 2 congruent sides
Find the values of the variables.
9. _______ a
d
120°
a
_______ b
f
_______ c
c
_______ d
e 115°
e
b
_______ e
_______ f
_______ g
20°
68°
g
102°
70°
40°
_______ j
_______ k
45°
j
50°
k
m
_______ m
2013-2014: Geometry Unit IV Review
Page 1
Classify each triangle by (s) sides and (a) angles.
10.
8
6
10
(s) ____________
(s) ____________
(s) ____________
(s) ____________
(a) ____________
(a) ____________
(a) ____________
(a) ____________
Solve for x and find the measure of each angle.
B
11.
(4x – 20)°
x = __________
m  A = __________
A
(6x – 60)°
(3x)°
C
m  B = __________
m  C = __________
True or False. Write out the word.
_______ 12. All equilateral triangles are isosceles triangles.
_______ 13. A triangle may have two right angles.
_______ 14. The acute angles of a right triangle are complementary.
Find the measure of each angle.
_______ 15. m  BCA
D
_______ 16. m  DCE
B
_______ 17. m  DEF
_______ 18. m  BCD
G
_______ 19. m  BAG
_______ 20. m  GAH
50°
A
H
C
E
F
For #15-20
2013-2014: Geometry Unit IV Review
Page 2
Name the congruence pattern that would prove the triangles congruent. You may mark
vertical angles or shared sides as necessary.
_______ 21. 21.
22.
23.
25.
26.
28.
29.
31.
32.
_______ 22.
_______ 23.
_______ 24. 24.
_______ 25.
_______ 26.
_______ 27. 27.
_______ 28.
_______ 29.
_______ 30. 30.
_______ 31.
_______ 32.
Is it possible for a triangle to have sides with the given lengths? Yes or No.
_______ 33. 3, 4, 7
_______ 34. 11, 12, 23
_______ 35. 8, 15, 27
_______ 36. 1.5, 2, 3.75
2013-2014: Geometry Unit IV Review
Page 3
Put the angles in order from largest to smallest
_______ 37.
37.
2m
_______
38.
X
A
17 ft
B
W
_______
3.9 m
29 ft
37 ft
2.8 m
_______ 38.
C
Y
_______
_______
Put the sides in order from smallest to largest.
_______ 39.
39.
_______
_______
T
40.
T
56º
S
17.
7Iº
_______ 40.
U
S
58º
62º
U
_______
_______
Informal Proofs.
41. MS  LS , ES  BS .
M
1
a. Mark the triangles with the given information.
b. What else is congruent?
B
E
S
2
L
c. Why are the triangles congruent?
2013-2014: Geometry Unit IV Review
Page 4
42. P is the midpt of RS , and  R   S.
T
R
a. Mark the triangles with the given information.
b. What else is congruent?
P
1
2
S
V
c. Why are the triangles congruent?
d. Explain why  T   V?
A
Formal Proofs
43.
F
4
3
Given:  1   2;  3   4; C is midpt of BE
Prove: ∆ABC  ∆FEC
1
B
2
A
44.
Given:  A   E; C is midpt of BD
B
1
Prove: ∆ACB  ∆ECD
2
D
E
C
C
E
2013-2014: Geometry Unit IV Review
Page 5
45. In ∆ CAT, CA = 12, AT = 15, and CT = 17. Which list has the angles of ∆CAT in order from smallest to largest?
A. ∡ C, ∡ A, ∡ T
B. ∡ A, ∡ C, ∡ T
C. ∡ T, ∡ C, ∡ A
D. ∡ T, ∡ A, ∡ C
46. Find m ∡ D
O
4x°
(9x-20)°
G
D
47. Find the measure of the smallest interior angle.
(5x-15)°
105°
(6x-12)°
48. Juan plans on drawing ∆QUE, such that the measure of ∡Q can range from 42° to 47°, and the measure of ∡ U can
range from 38° to 46°. Given these conditions, what is the correct range of measures possible for ∡E?
2013-2014: Geometry Unit IV Review
Page 6
49. In the figure below, ̅̅̅̅
̅̅̅̅̅ bisect each other at A.
B
T
A
M
N
Is ∆BAT ≅ ∆MAN? ______________
By what Triangle Congruence Postulate or Theorem? ________________________________________
What else must then also be true by CPCTC? _______________________________________________
____________________________________________________________________________________
2013-2014: Geometry Unit IV Review
Page 7