Download Unit 4 Corrective

Name: ________________________ Class: ___________________ Date: __________
Geometry - Chapter 4 Corrective #1 - 15-16
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
1. Apply the transformation M to the polygon with the given vertices.
Identify and describe the transformation.
M: (x, y) → (–x, –y)
A(–3, 6), B(–3, 1), C(1, 1), D(1, 6)
a.
c.
This is a rotation of 180° about the
origin.
b.
This is a reflection over the x-axis.
d.
This is a rotation of 90° clockwise about
the origin.
This is a rotation of 180° about the
origin.
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ID: A
____
2. For these triangles, select the triangle congruence statement and the postulate or theorem that supports it.
a.
b.
∆ABC ≅ ∆JLK , HL
∆ABC ≅ ∆JKL, HL
c.
d.
∆ABC ≅ ∆JLK , SAS
∆ABC ≅ ∆JKL, SAS
Short Answer
3. ∆ABC is an isosceles triangle. AB is the longest side with length 11x + 6. BC = 5x + 6 and CA = 4x + 9. Find
AB.
4. One of the acute angles in a right triangle has a measure of 34.6°. What is the measure of the other acute
angle?
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5. Determine whether the lines shown are parallel, perpendicular, or neither.
6. Show ∆ABD ≅ ∆CDB for a = 3.
7. Find m∠DCB, given ∠A ≅ ∠F , ∠B ≅ ∠E , and m∠CDE = 33.5°.
8. Find the measure of each numbered angle.
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9. Given that ∆ABC ≅ ∆DEC and m∠E = 23°, find m∠ACB.
Matching
Match each vocabulary term with its definition.
a. acute triangle
b. equilateral triangle
c. right triangle
d. obtuse triangle
e. isosceles triangle
f. equiangular triangle
g. scalene triangle
____ 10. a triangle with three congruent sides
____ 11. a triangle with one obtuse angle
____ 12. a triangle with at least two congruent sides
____ 13. a triangle with one right angle
____ 14. a triangle with three acute angles
Match each vocabulary term with its definition.
a. isosceles triangle
b. base angle
c. scalene triangle
d. equiangular triangle
e. triangle rigidity
f. base
g. legs of an isosceles triangle
____ 15. a triangle with three congruent angles
____ 16. a property of triangles that states that if the side lengths of a triangle are fixed, the triangle can have only one
shape
____ 17. one of the two angles that have the base of the triangle as a side
____ 18. one of the two congruent sides of the isosceles triangle
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____ 19. the side opposite the vertex angle of a triangle
Match each vocabulary term with its definition.
a. interior angle
b. complementary angles
c. supplementary angles
d. exterior angle
e. interior
f. remote interior angle
g. exterior
____ 20. the set of all points inside a polygon
____ 21. the set of all points outside a polygon
____ 22. an interior angle of a polygon that is not adjacent to the exterior angle
____ 23. an angle formed by one side of a polygon and the extension of an adjacent side
____ 24. an angle formed by two sides of a polygon with a common vertex
Match each vocabulary term with its definition.
a. exterior angle
b. corresponding angles
c. interior angle
d. included angle
e. vertex angle
f. included side
g. corresponding sides
____ 25. angles in the same relative position in two different polygons that have the same number of angles
____ 26. the common side of two consecutive angles of a polygon
____ 27. the angle formed by the legs of a triangle
____ 28. the angle formed by two adjacent sides of a polygon
____ 29. sides in the same relative position in two different polygons that have the same number of sides
Match each vocabulary term with its definition.
a. paragraph proof
b. two-column proof
c. coordinate proof
d. auxiliary line
e. congruent polygons
f. corollary
g. CPCTC
____ 30. a line drawn in a figure to aid in a proof
____ 31. two polygons whose corresponding sides and angles are congruent
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____ 32. a theorem whose proof follows directly from another theorem
____ 33. an abbreviation for “Corresponding Parts of Congruent Triangles are Congruent,” which can be used as a
justification in a proof after two triangles are proven congruent
____ 34. a style of proof that uses coordinate geometry and algebra
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ID: A
Geometry - Chapter 4 Corrective #1 - 15-16
Answer Section
MULTIPLE CHOICE
1. ANS: B
2. ANS: B
TOP: 4-1 Congruence and Transformations
TOP: 4-6 Triangle Congruence: ASA, AAS, and HL
SHORT ANSWER
3. ANS:
AB = 39
TOP: 4-2 Classifying Triangles
4. ANS:
55.4°
TOP: 4-3 Angle Relationships in Triangles
5. ANS:
neither
TOP: 4-7-Ext. Lines and Slopes
6. ANS:
[1] 3 + 7
[2] 4(3) − 2
[3] 16
[4] 16
[5] SSS
TOP: 4-5 Triangle Congruence: SSS and SAS
7. ANS:
m∠DCB = 33.5°
TOP: 4-3 Angle Relationships in Triangles
8. ANS:
m∠1 = 54°, m∠2 = 63°, m∠3 = 63°
TOP: 4-9 Isosceles and Equilateral Triangles
9. ANS:
m∠ACB = 67°
TOP: 4-4 Congruent Triangles
MATCHING
10. ANS: B
TOP: 4-2 Classifying Triangles
1
ID: A
11.
12.
13.
14.
ANS:
ANS:
ANS:
ANS:
D
E
C
A
TOP:
TOP:
TOP:
TOP:
4-2 Classifying Triangles
4-2 Classifying Triangles
4-2 Classifying Triangles
4-2 Classifying Triangles
15.
16.
17.
18.
19.
ANS:
ANS:
ANS:
ANS:
ANS:
D
E
B
G
F
TOP:
TOP:
TOP:
TOP:
TOP:
4-2 Classifying Triangles
4-5 Triangle Congruence: SSS and SAS
4-9 Isosceles and Equilateral Triangles
4-9 Isosceles and Equilateral Triangles
4-9 Isosceles and Equilateral Triangles
20.
21.
22.
23.
24.
ANS:
ANS:
ANS:
ANS:
ANS:
E
G
F
D
A
TOP:
TOP:
TOP:
TOP:
TOP:
4-3 Angle Relationships in Triangles
4-3 Angle Relationships in Triangles
4-3 Angle Relationships in Triangles
4-3 Angle Relationships in Triangles
4-3 Angle Relationships in Triangles
25.
26.
27.
28.
29.
ANS:
ANS:
ANS:
ANS:
ANS:
B
F
E
D
G
TOP:
TOP:
TOP:
TOP:
TOP:
4-4 Congruent Triangles
4-6 Triangle Congruence: ASA, AAS, and HL
4-9 Isosceles and Equilateral Triangles
4-5 Triangle Congruence: SSS and SAS
4-4 Congruent Triangles
30.
31.
32.
33.
34.
ANS:
ANS:
ANS:
ANS:
ANS:
D
E
F
G
C
TOP:
TOP:
TOP:
TOP:
TOP:
4-3 Angle Relationships in Triangles
4-4 Congruent Triangles
4-3 Angle Relationships in Triangles
4-7 Triangle Congruence: CPCTC
4-8 Introduction to Coordinate Proof
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