Name: ________________________ Class: ___________________ Date: __________
ID: A
Unit 7 Chapter 6 Test Review - GEOMETRY
1. What is the sum of the angle measures of a 23-gon?
2. The sum of the angle measures of a polygon with s sides is 3240. Find s.
3. A road sign is in the shape of a regular hexagon. What is the measure of each angle on the sign? Round to the
nearest tenth.
4. Find the missing values of the variables. The diagram is not to scale.
5. Find the value of x. The diagram is not to scale.
6. The sum of the measures of two exterior angles of a triangle is 278. What is the measure of the third exterior
angle?
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Name: ________________________
ID: A
7. Find the values of the variables in the parallelogram. The diagram is not to scale.
8. In the parallelogram, mKLO  78 and mMLO  23. Find mKJM. The diagram is not to scale.
9. In the parallelogram, mQRP  11 and mPRS  93. Find mPQR. The diagram is not to scale.
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Name: ________________________
ID: A
10. For the parallelogram, if m2  4x  27 and m4  3x  13, find m3. The diagram is not to scale.
11. LMNO is a parallelogram. If NM = x + 14 and OL = 2x + 6, find the value of x and then find NM and OL.
12. In the figure, the horizontal lines are parallel and AB  BC  CD. Find JM. The diagram is not to scale.
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Name: ________________________
ID: A
13. Find values of x and y for which ABCD must be a parallelogram. The diagram is not to
scale.
14. Based on the information in the diagram, can you prove that the figure is a parallelogram? Explain.
15. In the rhombus, m1  30x, m2  x  y, and m3  3z. Find the value of each variable. The diagram is
not to scale.
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Name: ________________________
ID: A
16. In the rhombus, m1  148. What are m2 and m3? The diagram is not to scale.
17. Find the measure of the numbered angles in the rhombus. The diagram is not to scale.
18. DEFG is a rectangle. DF = 6x – 1 and EG = x + 59. Find the value of x and the length of each diagonal.
19. In rectangle KLMN, KM = 6x  11 and LN = 68. Find the value of x.
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Name: ________________________
ID: A
20. In quadrilateral ABCD, AE  x  22 and BE  3x  18 . For what value of x is ABCD a rectangle?
21. Find the values of a and b. The diagram is not to scale.
22. J and M are base angles of isosceles trapezoid JKLM. If mJ  15x  9, and
mM  13x  13, find mK.
23. LM is the midsegment of
ABCD. AB  44 and DC  118. What is LM?
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Name: ________________________
24. LM is the midsegment of
ID: A
ABCD. AB  x  8, LM  4x  3, and DC  306. What is the value of x?
25. Find m1 and m3 in the kite. The diagram is not to scale.
26. mR  150 and mS  100. Find mT. The diagram is not to scale.
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ID: A
Unit 7 Chapter 6 Test Review - GEOMETRY
Answer Section
1. ANS:
3780
PTS:
OBJ:
NAT:
KEY:
2. ANS:
20
1
DIF: L3
REF: 6-1 The Polygon Angle-Sum Theorems
6-1.1 To find the sum of the measures of the interior angles of a polygon
CC G.SRT.5| M.1.d| G.3.f
TOP: 6-1 Problem 1 Finding a Polygon Angle Sum
Polygon Angle-Sum Theorem
PTS:
OBJ:
NAT:
KEY:
3. ANS:
120
1
DIF: L3
REF: 6-1 The Polygon Angle-Sum Theorems
6-1.1 To find the sum of the measures of the interior angles of a polygon
CC G.SRT.5| M.1.d| G.3.f
TOP: 6-1 Problem 1 Finding a Polygon Angle Sum
Polygon Angle-Sum Theorem
PTS: 1
DIF: L3
REF: 6-1 The Polygon Angle-Sum Theorems
OBJ: 6-1.1 To find the sum of the measures of the interior angles of a polygon
NAT: CC G.SRT.5| M.1.d| G.3.f
TOP: 6-1 Problem 2 Using the Polygon Angle-Sum
KEY: Corollary to the Polygon Angle-Sum Theorem | regular polygon
4. ANS:
x = 128, y = 58
PTS:
OBJ:
NAT:
KEY:
5. ANS:
45
1
DIF: L3
REF: 6-1 The Polygon Angle-Sum Theorems
6-1.1 To find the sum of the measures of the interior angles of a polygon
CC G.SRT.5| M.1.d| G.3.f
TOP: 6-1 Problem 3 Using the Polygon Angle-Sum Theorem
exterior angle | Polygon Angle-Sum Theorem
PTS:
OBJ:
NAT:
KEY:
6. ANS:
82
1
DIF: L4
REF: 6-1 The Polygon Angle-Sum Theorems
6-1.1 To find the sum of the measures of the interior angles of a polygon
CC G.SRT.5| M.1.d| G.3.f
TOP: 6-1 Problem 3 Using the Polygon Angle-Sum Theorem
Polygon Angle-Sum Theorem
PTS:
OBJ:
NAT:
KEY:
1
DIF: L3
REF: 6-1 The Polygon Angle-Sum Theorems
6-1.2 To find the sum of the measures of the exterior angles of a polygon
CC G.SRT.5| M.1.d| G.3.f
TOP: 6-1 Problem 4 Finding an Exterior Angle Measure
exterior angle | Polygon Angle-Sum Theorem
1
ID: A
7. ANS:
x  25, y  51, z  104
PTS:
OBJ:
NAT:
TOP:
KEY:
8. ANS:
101
1
DIF: L4
REF: 6-2 Properties of Parallelograms
6-2.1 To use relationships among sides and angles of parallelograms
CC G.CO.11| CC G.SRT.5| G.1.c| G.3.f
6-2 Problem 1 Using Consecutive Angles
parallelogram | opposite angles | consecutive angles | transversal
PTS:
OBJ:
NAT:
TOP:
9. ANS:
76
1
DIF: L4
REF: 6-2 Properties of Parallelograms
6-2.1 To use relationships among sides and angles of parallelograms
CC G.CO.11| CC G.SRT.5| G.1.c| G.3.f
6-2 Problem 1 Using Consecutive Angles
KEY: parallelogram | opposite angles
PTS:
OBJ:
NAT:
TOP:
10. ANS:
151
1
DIF: L4
REF: 6-2 Properties of Parallelograms
6-2.1 To use relationships among sides and angles of parallelograms
CC G.CO.11| CC G.SRT.5| G.1.c| G.3.f
6-2 Problem 1 Using Consecutive Angles
KEY: parallelogram | consecutive angles
PTS: 1
DIF: L4
REF: 6-2 Properties of Parallelograms
OBJ: 6-2.1 To use relationships among sides and angles of parallelograms
NAT: CC G.CO.11| CC G.SRT.5| G.1.c| G.3.f
TOP: 6-2 Problem 1 Using Consecutive Angles
KEY: algebra | parallelogram | opposite angles | consecutive angles
11. ANS:
x = 8, NM = 22, OL = 22
PTS:
OBJ:
NAT:
TOP:
12. ANS:
15
PTS:
OBJ:
NAT:
TOP:
1
DIF: L2
REF: 6-2 Properties of Parallelograms
6-2.1 To use relationships among sides and angles of parallelograms
CC G.CO.11| CC G.SRT.5| G.1.c| G.3.f
6-2 Problem 3 Using Algebra to Find Lengths
KEY: parallelogram | algebra
1
DIF: L3
REF: 6-2 Properties of Parallelograms
6-2.1 To use relationships among sides and angles of parallelograms
CC G.CO.11| CC G.SRT.5| G.1.c| G.3.f
6-2 Problem 4 Using Parallel Lines and Transversals
KEY: transversal | parallel lines
2
ID: A
13. ANS:
x = 5, y = 8
PTS: 1
DIF: L3
REF: 6-3 Proving That a Quadrilateral Is a Parallelogram
OBJ: 6-3.1 To determine whether a quadrilateral is a parallelogram
NAT: CC G.CO.11| CC G.SRT.5| G.1.c| G.3.f
TOP: 6-3 Problem 1 Finding Values for Parallelograms
KEY: algebra | parallelogram
14. ANS:
Yes; both pairs of opposite sides are congruent.
PTS: 1
DIF: L2
REF: 6-3 Proving That a Quadrilateral Is a Parallelogram
OBJ: 6-3.1 To determine whether a quadrilateral is a parallelogram
NAT: CC G.CO.11| CC G.SRT.5| G.1.c| G.3.f
TOP: 6-3 Problem 2 Deciding Whether a Quadrilateral Is a Parallelogram
KEY: opposite angles | parallelogram
15. ANS:
x = 3, y = 87, z = 30
PTS: 1
DIF: L4
REF: 6-4 Properties of Rhombuses, Rectangles, and Squares
OBJ: 6-4.2 To use properties of diagonals of rhombuses and rectangles
NAT: CC G.CO.11| CC G.SRT.5| G.1.c| G.3.f
TOP: 6-4 Problem 2 Finding Angle Measures
KEY: algebra | diagonal | rhombus
16. ANS:
m2 = 148, m3  16
PTS: 1
DIF: L3
REF: 6-4 Properties of Rhombuses, Rectangles, and Squares
OBJ: 6-4.2 To use properties of diagonals of rhombuses and rectangles
NAT: CC G.CO.11| CC G.SRT.5| G.1.c| G.3.f
TOP: 6-4 Problem 2 Finding Angle Measures
KEY: diagonal | rhombus
17. ANS:
m1  90, m2 = 35, and m3  55
PTS: 1
DIF: L3
REF: 6-4 Properties of Rhombuses, Rectangles, and Squares
OBJ: 6-4.2 To use properties of diagonals of rhombuses and rectangles
NAT: CC G.CO.11| CC G.SRT.5| G.1.c| G.3.f
TOP: 6-4 Problem 2 Finding Angle Measures
KEY: diagonal | rhombus
18. ANS:
x = 12, DF = 71, EG = 71
PTS:
OBJ:
NAT:
TOP:
1
DIF: L3
REF: 6-4 Properties of Rhombuses, Rectangles, and Squares
6-4.2 To use properties of diagonals of rhombuses and rectangles
CC G.CO.11| CC G.SRT.5| G.1.c| G.3.f
6-4 Problem 3 Finding Diagonal Length
KEY: rectangle | algebra | diagonal
3
ID: A
19. ANS:
9.5
PTS:
OBJ:
NAT:
TOP:
20. ANS:
20
1
DIF: L2
REF: 6-4 Properties of Rhombuses, Rectangles, and Squares
6-4.2 To use properties of diagonals of rhombuses and rectangles
CC G.CO.11| CC G.SRT.5| G.1.c| G.3.f
6-4 Problem 3 Finding Diagonal Length
KEY: rectangle | algebra | diagonal
PTS: 1
DIF: L3
REF: 6-5 Conditions for Rhombuses, Rectangles, and Squares
OBJ: 6-5.1 To determine whether a parallelogram is a rhombus or rectangle
NAT: CC G.CO.11| CC G.SRT.5| G.1.c| G.3.f
TOP: 6-5 Problem 2 Using Properties of Special Parallelograms
KEY: parallelogram | rectangle | reasoning
21. ANS:
a  137, b  71
PTS: 1
DIF: L2
REF: 6-6 Trapezoids and Kites
OBJ: 6-6.1 To verify and use properties of trapezoids and kites NAT: CC G.SRT.5| G.1.c| G.3.f
TOP: 6-6 Problem 1 Finding Angle Measures in Trapezoids
KEY: trapezoid | base angles
22. ANS:
141
PTS:
OBJ:
TOP:
KEY:
23. ANS:
81
1
DIF: L4
REF: 6-6 Trapezoids and Kites
6-6.1 To verify and use properties of trapezoids and kites NAT: CC G.SRT.5| G.1.c| G.3.f
6-6 Problem 2 Finding Angle Measures in Isosceles Trapezoids
algebra | isosceles trapezoid | base angles | trapezoid
PTS:
OBJ:
TOP:
KEY:
24. ANS:
44
1
DIF: L2
REF: 6-6 Trapezoids and Kites
6-6.1 To verify and use properties of trapezoids and kites NAT: CC G.SRT.5| G.1.c| G.3.f
6-6 Problem 3 Using the Midsegment of a Trapezoid
trapezoid | base angles | midsegment of a trapezoid
PTS: 1
DIF: L3
REF: 6-6 Trapezoids and Kites
OBJ: 6-6.1 To verify and use properties of trapezoids and kites NAT: CC G.SRT.5| G.1.c| G.3.f
TOP: 6-6 Problem 3 Using the Midsegment of a Trapezoid
KEY: trapezoid | base angles | midsegment of a trapezoid
25. ANS:
m 1  26, m3  64
PTS: 1
DIF: L3
REF: 6-6 Trapezoids and Kites
OBJ: 6-6.1 To verify and use properties of trapezoids and kites NAT: CC G.SRT.5| G.1.c| G.3.f
TOP: 6-6 Problem 4 Finding Angle Measures in Kites
KEY: kite | diagonal
4
ID: A
26. ANS:
10
PTS: 1
DIF: L2
REF: 6-6 Trapezoids and Kites
OBJ: 6-6.1 To verify and use properties of trapezoids and kites NAT: CC G.SRT.5| G.1.c| G.3.f
TOP: 6-6 Problem 4 Finding Angle Measures in Kites
KEY: kite | sum of interior angles
5