page 1
Geometry – Workbook 6, Part 1 Worksheet G6-1 page 145 1.
2.
3.
2.
D
22º, 79º, 79º with 5.2 cm, 5.2 cm, 2.1 cm side lengths
E
120º, 35º, 25º with 3.1 cm, 6 cm, 4 cm side lengths
Obtuse; 120º
1.
Teacher to check.
d)
Obtuse; 150º
2.
Teacher to check.
a)
Acute; 60º
3.
c)
7; 7
d)
5; 5
b)
Acute; 40º
e)
8; 8
c)
Obtuse; 115º
f)
10; 10
d)
Acute; 30º
a)
3
e)
Acute; 40º
b)
4
f)
Obtuse; 137º
c)
5
g)
Obtuse; 125º
d)
6
h)
Acute; 20º
a)
30º
a)
Teacher to check.
b)
In each triangle, two sides are the same length.
c)
(i)
Obtuse-angled (or Isosceles – see G6-8)
(ii)
Acute-angled (or Equilateral – see G6-8)
Shapes
Letters
Triangles
C
b)
130º
B, D, F, G, H
c)
45º
d)
45º
4.
Teacher to check.
Pentagons
A
e)
105º
5.
Hexagons
E, I
f)
90º
Two congruent right-angled triangles
6.
Teacher to check.
Answers will vary.
5.
37 sides
Worksheet G6-2 page 146 a)
Worksheet G6-4 page 150 Teacher to check.
Less than
Worksheet G6-5 page 151
Greater than
1.
3.
Teacher to check.
4.
Teacher to check.
Worksheet G6-3 page 147 a)
Acute
b)
Obtuse
c)
Acute
d)
Acute
e)
Obtuse
f)
Obtuse
g)
Obtuse
h)
Actute
i)
Obtuse
3.
2.
a)
a)
∠ABC: 48º
b)
∠ABC: 42º
Scalene: A, E Right-angled: A Both: A Neither: B, C, D
b)
Obtuse: E, B
∠XYZ: 122º
Obtuse-angled
a)
110º, 30º, 45º; Obtuse-angled
b)
90º, 45º, 45º; Right-angled
c)
60º, 50º, 70º; Acuteangled
a)
About 110º, 110º, 110º, 110º, 110º; VD – “at least one obtuse angle”
c)
A, E
c)
e)
b)
Scalene
Acute-angled
d)
2 right angles
B, D
Neither: A, C
2 right angles
e)
C
Isosceles
∠XYZ: 110º
a)
2 right angles
Equilateral
b)
Less than
1 right angle
A
Both: B
d)
d)
Rightangled
∠XYZ: 110º
c)
c)
B, E
Obtuse-angled
Right angle
2.
Obtuseangled
∠ABC: 90º
Right-angled
No right angles
C, D
a)
b)
b)
Acuteangled
Worksheet G6-7 page 153 1.
Triangles with Property
c)
Acute-angled
c)
(iii) Right-angled (or Isosceles – see G6-8)
Property
Isosceles: D, B
a)
b)
1.
60º angles with 3 cm side lengths
Acute; 30º
6; 6
4.
C
c)
b)
3.
Worksheet G6-6 page 152
b)
5; 5
4.
2.
Acute; 60º
a)
Quadrilaterals
1.
a)
60º, 60º, 60º; VD – “at least one acute angle” 70º, 115º, 70º, 115º; VD – “at least one obtuse angle” and ”at least one acute angle”
The pentagon (A) has all obtuse angles.
2.
3.
∠AEB = 45º ∠BEC = 21º ∠CED = 59º From least to greatest: ∠BEC, ∠AEB, ∠CED
4.
acute angles: ∠AED, ∠BEC obtuse angles: ∠AEB, ∠CED
Worksheet G6-8 page 154
3.
1.
Teacher to check.
2.
a)
Right-angled; Isosceles
b)
Obtuse-angled; Scalene
3.
A
52º, 90º, 38º with 3 cm, 4 cm, 5 cm side lengths
B
110º, 35º, 35º with 4 cm, 6.5 cm, 4 cm side lengths
1.
a) and c) should be marked as parallel BONUS: e)
If the pair of lines in b) are extended, they will intersect so aren’t parallel. By definition, the lines in d) cannot be parallel as they are curved.
2.
For use with JUMP Math’s Workbook 6 Part 1 (3rd Edition) ISBN 978-1-897120-48-4
x = 30º
Worksheet G6-10 page 156
NOTE: Side lengths and angles are recorded clockwise, from left to right. 1.
Teacher to check.
Worksheet G6-9 page 155
Teacher to check.
Selected Answer Key – Workbook 6 1
page 2
Geometry – Workbook 6, Part 1 (continued) 3.
4.
a)
1
b)
2
c)
3
d)
1
e)
2
f)
2
g)
0
h)
0
4.
b)
c)
Teacher to check.
5.
Teacher to check.
6.
E has three lines that are parallel; H and M each have a pair of parallel lines; W and K have no parallel lines.
Worksheet G6-11 page 158 1.
2.
d)
5.
a)
b)
3.
3 cm, 3 cm, 3 cm, 3 cm; (equilateral) 1.7 cm, 1.7 cm, 1.7 cm, 1.7 cm, 1.7 cm; (equilateral) 2 cm, 2 cm, 2 cm, 2 cm; (equilateral)
Property
4.
5.
Shapes with Property
Teacher to check. a)
Rectangle
b)
Parallelogram
c)
Square
d)
Rhombus
Rectangle
a)
2 pairs; rectangle
Worksheet G6-13 page 162
b)
2 pairs; parallelogram
1.
c)
2 pairs; square
d)
1 pair; trapezoid
Equilateral
A, B, D, F, I
Not Equilateral
C, E, G, H, J
No right ∠
A, D, F, G, I
6.
Answers will vary.
7.
a)
All No
b)
3 right ∠
J
c)
No
4 right ∠
B, C
d)
Some
No obtuse ∠
a)
Rhombus
A, B, C, E, G
b)
Rectangle
c)
Trapezoid
2 pairs
c)
F
No pairs
G
1 pair
H
2 pairs d)
No Pairs: F
Property No right angles
2 right angles 4 right angles
Shapes with Property D, E, I, J C A, B, G, K
e)
F, H
No parallel C, I, J lines 1 pair
A, B, D, G, K
2 pairs
E, F, H
8.
1 or more obtuse ∠
D, F, H, I, J
No parallel sides
A, E, F
1 pair of parallel sides
G, H
2 pairs of parallel sides
B, C, D, J
12. a)
b)
3 pairs of parallel sides
I
Triangles
A, E
Quadrilaterals
B, C, D
Pentagons
F, H
Hexagons
I, J
a)
3 cm, 2 cm, 3 cm, 2 cm; parallelogram
b)
2 cm, 2 cm, 2 cm, 2 cm; square
For use with JUMP Math’s Workbook 6 Part 1 (3rd Edition) ISBN 978-1-897120-48-4
c)
A parallelogram has two pairs of parallel lines, each line of a pair are equal in length. A trapezoid has one pair of parallel lines, each line in the pair may differ in length.
b)
no
c)
no
d)
no
3.
The intersection of the diagonals is perpendicular.
4.
a)
B, D
b)
The diagonals bisect at 90º. One of the two diagonals is the line of symmetry.
5.
The angles opposite the line of symmetry are equal.
6.
Diagonals meet at right angles (only): C Two pairs of equal adjacent sides (only): none
Both have two pairs of parallel sides. A rhombus has 4 equal sides. Both have two pairs of parallel sides and all sides. A rhombus may not have all 90º angles. A square has 4 right angles.
yes
Teacher to check.
Rectangle, parallelogram, rhombus
10. Square, rectangle
a)
2.
11. Square, rhombus
Worksheet G6-12 page 160 1.
9.
In a trapezoid, only 1 pair of sides is parallel.
d)
H
1 pair
c)
Rhombus
2 right ∠
E
A rectangle does not have all equal sides.
c)
E
D
b)
Parallelogram Square
1 right ∠
1 pair
A square is a parallelogram with 4 right angles (so it is also a rectangle). It has one extra property: equal sides.
a)
2 pairs
C
13. a)
b)
B
1 right angle
b)
2.
2 pairs
Two Pairs: A, B, E, H
a)
4 cm, 2.5 cm, 4 cm, 2.5 cm; (not equilateral)
A
One Pair: C, D, G
3.
a)
Inside: A, E, F Outside: B, D 7.
a)
square
b)
rhombus
c)
square
d)
rhombus
Worksheet G6-14 page 163 1.
2.
a)
Not congruent
b)
Congruent
c)
Congruent
a)
No; size is different.
b)
Yes; same shape and size.
Selected Answer Key – Workbook 6 2
page 3
Geometry – Workbook 6, Part 1 (continued) 3.
a)
b)
Teacher to check (must be same size and shape as original).
a)
6
b)
15
c)
12
d)
20
a)
A: 3 possible shapes
Length of B will be 4 units.
b)
B: 5 possible shapes
Length of B will be 6 units.
c)
Length of B will be 6 units.
Answers will vary.
4.
Teacher to check.
5.
a)
C: 1 possible shapes 6.
7.
b)
B
a)
∠BAC or ∠CAB
b)
∠DFE or ∠EFD
c)
∠IHJ or ∠JHI
d)
∠MKL = ∠LKM
a)
If rounding to the nearest cm, all triangles will have sides of length 3 cm, 5 cm and 6 cm.
b)
∆ABC: 25º, 50º, 105º ∆DEF: 30º, 60º, 90º ∆HIJ: 30º, 60º, 90º ∆KLM: 25º, 50º, 105º
8.
9.
3.
4.
5.
2 units
6.
A and C
7.
No
8. 9.
2.
Obtuse ∠
√
Lines of symmetry
√
Equilateral
√
Teacher to check.
Regular Pentagon −5
A shape has rotation symmetry of order equal to the number of lines of symmetry.
8.
No, the shapes are not mirror images.
Teacher to check.
9.
Answers will vary.
Worksheet G6-17 page 170
Teacher to check.
2.
Teacher to check.
3.
c)
2
a)
Teacher to check.
d)
6
e)
5
f)
4
g)
2
h)
1
5.
The 2nd and 5th should be shaded.
6.
a)
b)
1.
F1 a)
F2
S?
Figures
1
B, C, F, H
2
B, C, F
c)
Prop
Figures
1
A, C, D, E, F, H
2
C, F
2.
D?
4
√
3
4
√
1
C, H Prop
C & F have both properties.
3 0
a) b)
B, C & F have both properties.
For example, an equilateral triangle has rotation symmetry of order 3.
Worksheet G6-16 page 167 1.
1.
Regular Hexagon −6
13. No: similar figures must have the same angles and – since a trapezoid can only have one set of parallel lines – this will never be the case.
Answers will vary.
4
√
Worksheet G6-18 page 171
c)
d)
Acute ∠
3.
3
5
√
Square − 4
5
c)
Right ∠
Triangle − 3
a)
3
The number of edges is equal to the number of lines of symmetry.
√
Q
E
2+ 90º
O
A
Y
N
Y
N
Y
Y
Y
N
N
N
Y
Y
C
Y
N
Y
Y
N
N
D
N
Y
Y
N
N
Y
E
N
Y
N
N
N
Y
3.
Answers will vary.
0
2
√
3
1
√
0
1
√
Worksheet G6-19 page 173
3
0
√
1.
Y
N
√
F; F; F; F;
b)
F; F; T; T;
More than two lines of symmetry: A, E
c)
F; F; T; T;
C, B
d)
T; T; F; T;
For use with JUMP Math’s Workbook 6 Part 1 (3rd Edition) ISBN 978-1-897120-48-4
A
B
a)
Less than two lines of symmetry: B, C, D, F, G
D?
√
A & H are congruent; A & H are both similar to F.
b)
3
√
A and C are similar.
Answers will vary.
a)
Edges
Answers will vary.
b)
b)
c)
√
Pairs of parallel pides
Hexagon − 6; 6 b)
Vertices
2.
∆ABC and ∆KLM; ∆DEF and ∆HIJ
In rectangle A, the longer side is double the shorter side. Hence, in triangle B, the missing side is 2 × 2 = 4 cm.
b)
Pentagon − 5; 5
12. Answers will vary.
Teacher to check.
S?
Square − 4; 4
11. Answers will vary.
4.
Number of edges; number of lines of symmetry: Equilateral triangle − 3; 3
10. Answers will vary.
Worksheet G6-15 page 165 1.
a)
Order of rotation symmetry:
a)
b)
7.
Selected Answer Key – Workbook 6 3
page 4
Geometry – Workbook 6, Part 1 (continued)
2.
3.
4.
e)
T; F; T; F;
f)
F; T; T; F
a)
Equilateral triangle
b)
Isosceles triangle
c)
Parallelogram
d)
Trapezoid
a)
Teacher to check.
b)
Teacher to check.
c)
Teacher to check.
a)
Teacher to check.
b)
Teacher to check.
Worksheet G6-20 page 174 1.
Teacher to check.
2.
Teacher to check.
3.
Teacher to check.
4.
5.
a)
∠ABC
b)
If line is perfectly diagonal and bisects a 90º angle, the angle will be 45º.
1 name: B (parallelogram), E (trapezoid) 2 names: C (rectangle, parallelogram), D (rhombus, parallelogram) 4 names: A (parallelogram, rectangle, square, rhombus)
6.
7.
a)
3 acute angles
b)
2 acute angles and 1 obtuse angle
c)
2 acute angles and 1 right angle
a)
Equilateral triangle
b)
Obtuse-angled triangle
For use with JUMP Math’s Workbook 6 Part 1 (3rd Edition) ISBN 978-1-897120-48-4
Selected Answer Key – Workbook 6 4