Download Unit 4 Review - Warren Local School District

Name: ________________________ Class: ___________________ Date: __________
ID: A
Geometry - Chapter 4 Review 15-16
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
____
1. a triangle with three acute angles
____
2. a triangle with one obtuse angle
____
3. a triangle with three congruent sides
____
4. a triangle with one right angle
____
5. a triangle with at least two congruent sides
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
____
6. a property of triangles that states that if the side lengths of a triangle are fixed, the triangle can have only one
shape
____
7. a triangle with three congruent angles
____
8. the side opposite the vertex angle of a triangle
____
9. one of the two angles that have the base of the triangle as a side
____ 10. one of the two congruent sides of the isosceles triangle
1
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
____ 11. an angle formed by one side of a polygon and the extension of an adjacent side
____ 12. an angle formed by two sides of a polygon with a common vertex
____ 13. an interior angle of a polygon that is not adjacent to the exterior angle
____ 14. the set of all points outside a polygon
____ 15. the set of all points inside a polygon
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
____ 16. angles in the same relative position in two different polygons that have the same number of angles
____ 17. the angle formed by the legs of a triangle
____ 18. the common side of two consecutive angles of a polygon
____ 19. sides in the same relative position in two different polygons that have the same number of sides
____ 20. the angle formed by two adjacent sides of a polygon
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
____ 21. a style of proof that uses coordinate geometry and algebra
____ 22. two polygons whose corresponding sides and angles are congruent
____ 23. a theorem whose proof follows directly from another theorem
2
____ 24. 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
____ 25. a line drawn in a figure to aid in a proof
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____ 26. Determine whether triangles
a.
b.
c.
d.
EFG and
The triangles are congruent because
(x,y) → (−x,y).
The triangles are congruent because
(x,y) → (−y,−x).
The triangles are congruent because
(x,y) → (x,−y).
The triangles are congruent because
(x,y) → (−y,x).
PQR are congruent.
EFG can be mapped to
PQR by a reflection:
EFG can be mapped to
PQR by a rotation:
EFG can be mapped to
PQR by a reflection:
EFG can be mapped to
PQR by a rotation:
3
____ 27. Tom is wearing his favorite bow tie to the school dance. The bow tie is in the shape of two triangles.
Given: AB ≅ ED , BC ≅ DC , AC ≅ EC , ∠A ≅ ∠E
Prove: ∆ABC ≅ ∆EDC
Complete the proof.
Proof:
Statements
1. AB ≅ ED , BC ≅ DC , AC ≅ EC
2. ∠A ≅ ∠E
3. ∠BCA ≅ ∠DCE
4. ∠B ≅ ∠D
5. [3]
Reasons
1. Given
2. Given
3. [1]
4. [2]
5. Definition of congruent triangles
a.
c.
b.
[1] Reflexive Angles Theorem
[2] Third Angles Theorem
[3] ∆ABC ≅ ∆EDC
[1] Third Angles Theorem
[2] Vertical Angles Theorem
[3] ∠ABC ≅ ∠EDC
d.
[1] Vertical Angles Theorem
[2] Third Angles Theorem
[3] ∠ABC ≅ ∠EDC
[1] Vertical Angles Theorem
[2] Third Angles Theorem
[3] ∆ABC ≅ ∆EDC
____ 28. Using the information about John, Jason, and Julie, can you uniquely determine the distances from John to
Julie and from Julie to Jason? Explain your answer.
Statement 1: John and Jason are standing 12 feet apart.
Statement 2: The angle from Julie to John to Jason measures 31°.
Statement 3: The angle from John to Jason to Julie measures 49°.
a.
b.
c.
d.
No. There is no unique configuration.
Yes. They form a unique triangle by SAS.
Yes. They form a unique triangle by ASA.
Yes. They form a unique triangle by SSS.
4
____ 29. Show ∆ABD ≅ ∆CDB for a = 3.
Complete the proof.
AB = a + 7 = [1] = 10
CD = 4a − 2 = [2] = 12 − 2 = 10
AD = 6a − 2 = 6(3) − 2 = 18 − 2 = [3]
CB = [4]
AB ≅ CD. AD ≅ CB. BD ≅ BD by the Reflexive Property of Congruence. So ∆ABD ≅ ∆CDB by [5].
a.
[1] a + 7
[2] 4a − 2
[3] 16
[4] 16
[5] SAS
c.
[1] 3 + 7
[2] 4(3) − 2
[3] 16
[4] 16
[5] SAS
b.
[1] 3 + 7
[2] 4(3) − 2
[3] 26
[4] 26
[5] SSS
d.
[1] 3 + 7
[2] 4(3) − 2
[3] 16
[4] 16
[5] SSS
Short Answer
30. Classify ∆ABC by its side lengths.
5
31. Two Seyfert galaxies, BW Tauri and M77, represented by points A and B, are equidistant from Earth,
represented by point C. What is m∠A?
32. Find the value of x.
33. Find m∠K .
34. Find m∠DCB, given ∠A ≅ ∠F , ∠B ≅ ∠E , and m∠CDE = 46°.
6
35. Given that ∆ABC ≅ ∆DEC and m∠E = 23°, find m∠ACB.
36. ∆ABF ≅ ∆EDG. ∆ABF and ∆GCF are equilateral. AG = 21 and CG =
1
4
AB. Find the total distance from A to
B to C to D to E.
37. Write an equation for the line parallel to the line shown that passes through the point (–2, 3).
7
ID: A
Geometry - Chapter 4 Review 15-16
Answer Section
MATCHING
1.
2.
3.
4.
5.
ANS:
ANS:
ANS:
ANS:
ANS:
A
D
B
C
E
TOP:
TOP:
TOP:
TOP:
TOP:
4-2 Classifying Triangles
4-2 Classifying Triangles
4-2 Classifying Triangles
4-2 Classifying Triangles
4-2 Classifying Triangles
6.
7.
8.
9.
10.
ANS:
ANS:
ANS:
ANS:
ANS:
E
D
F
B
G
TOP:
TOP:
TOP:
TOP:
TOP:
4-5 Triangle Congruence: SSS and SAS
4-2 Classifying Triangles
4-9 Isosceles and Equilateral Triangles
4-9 Isosceles and Equilateral Triangles
4-9 Isosceles and Equilateral Triangles
11.
12.
13.
14.
15.
ANS:
ANS:
ANS:
ANS:
ANS:
D
A
F
G
E
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
16.
17.
18.
19.
20.
ANS:
ANS:
ANS:
ANS:
ANS:
B
E
F
G
D
TOP:
TOP:
TOP:
TOP:
TOP:
4-4 Congruent Triangles
4-9 Isosceles and Equilateral Triangles
4-6 Triangle Congruence: ASA, AAS, and HL
4-4 Congruent Triangles
4-5 Triangle Congruence: SSS and SAS
21.
22.
23.
24.
25.
ANS:
ANS:
ANS:
ANS:
ANS:
C
E
F
G
D
TOP:
TOP:
TOP:
TOP:
TOP:
4-8 Introduction to Coordinate Proof
4-4 Congruent Triangles
4-3 Angle Relationships in Triangles
4-7 Triangle Congruence: CPCTC
4-3 Angle Relationships in Triangles
TOP:
TOP:
TOP:
TOP:
4-1 Congruence and Transformations
4-4 Congruent Triangles
4-6 Triangle Congruence: ASA, AAS, and HL
4-5 Triangle Congruence: SSS and SAS
MULTIPLE CHOICE
26.
27.
28.
29.
ANS:
ANS:
ANS:
ANS:
C
D
C
D
1
ID: A
SHORT ANSWER
30. ANS:
equilateral triangle
TOP: 4-2 Classifying Triangles
31. ANS:
m∠A = 65°
TOP: 4-9 Isosceles and Equilateral Triangles
32. ANS:
x=6
TOP: 4-7 Triangle Congruence: CPCTC
33. ANS:
m∠K = 63°
TOP: 4-3 Angle Relationships in Triangles
34. ANS:
m∠DCB = 46°
TOP: 4-3 Angle Relationships in Triangles
35. ANS:
m∠ACB = 67°
TOP: 4-4 Congruent Triangles
36. ANS:
98
TOP: 4-4 Congruent Triangles
37. ANS:
y = −3x – 3
TOP: 4-7-Ext. Lines and Slopes
2