Mathletics workbook Reasoning in Geometry Book 2 Student.pdf
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Reasoning Reasoni ng in geometry n t S t ude
Book - Ser i ie s e I 2
x
70
70
Mathlecs Instant Workbooks
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Reasoning in geometry Student Book - Series I 2 Contents Topics
Date completed
Topic 1 - Some basic ideas in geometry
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Topic 2 - Complementary, supplementary and vertically opposite angles
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Topic 3 - Angles and the value of pronumerals
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Topic 4 - Parallel lines and angles
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Topic 5 - Triangles and the value of pronumerals
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Topic 6 - Quadrilaterals and the value of pronumerals
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Topic 7 - Miscellaneous questions
__/__/__
Topic 8 - Deductive geometry
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Topic 9 - Problem solving and geometry
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Practice Tests Topic 1 - Topic test A
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Topic 2 - Topic test B
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Topic 3 - Topic test C
__/__/__
Author of The Topics and Topic Tests: AS Kalra
Reasoning in geometry Mathletics Instant Workbooks – Series I 2
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Reasoning in geometry Topic 1: Some basic ideas in geometry QUESTION 1
Complete the following sentences.
a
An equilateral triangle is a triangle in which _______________ sides are equal.
b
An isosceles triangle is a triangle in which _______________ sides are equal.
c
An scalene triangle is a triangle in which _______________ sides are equal.
d
An acute-angled triangle has _______________ acute angle(s).
e
An obtuse-angled triangle has _______________ obtuse angle(s).
f
A right-angled triangle has _______________ right angle(s).
QUESTION 2
Complete the following statements.
a
The interior angles of an equilateral triangle are _______________ .
b
The base angles of an isosceles triangle are _______________ .
c
The angle sum of a triangle is _______________ .
d
A triangle has all angles of equal size. The size of each angle is _______________ .
e
An exterior angle of a triangle is always equal to the sum of ____________________________ angles.
f
The angle sum of a quadrilateral is _______________ .
QUESTION 3
Complete the following.
a
A quadrilateral is a ______________________________ plane figure.
b
A polygon is a closed figure with ______________________________ sides.
c
A trapezium is a quadrilateral with one pair of opposite sides _______________ .
d
A parallelogram is a quadrilateral with both pairs of opposite sides _______________ .
e
A rhombus is a parallelogram in which all sides are _______________ .
f
A rectangle is a parallelogram in which each angle is a ______________________________ .
QUESTION 4
Complete the following sentences.
a
A square is a quadrilateral with all sides _______________ and each angle is _______________ .
b
A kite is a quadrilateral with two pairs of adjacent sides ______________ and no sides _____________ .
c
The angle sum of a kite is _______________ .
d
Opposite angles of a parallelogram are _______________ .
e
Each angle of a rectangle is equal to _______________ .
QUESTION 5
Complete the following statements.
a
Vertically opposite angles are _______________ .
b
Alternate angles are _______________ .
c
Corresponding angles are _______________ .
d
Co-interior angles add up to _______________ .
Reasoning in geometry Mathletics Instant Workbooks – Series I 2
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1
Reasoning in geometry Topic 2: Complementary, supplementary and vertically opposite angles QUESTION 1
Find the value of the pronumeral in each of the following.
a
b
c
127
°
54
°
105
°
x °
x °
x °
________________________
________________________
________________________
________________________
________________________
________________________
d
e
f
2t
°
y °
x °
120
°
136
70
°
m°
°
________________________
________________________
________________________
________________________
________________________
________________________
QUESTION 2
Find the value of the pronumeral and give reasons to justify your answer.
a
b
c
160 (2 x + 10) °
y °
x °
°
58
°
40
°
x °
________________________
________________________
________________________
________________________
________________________
________________________
d
e
(2a + 10)
°
f 110°
x °
72°
150
°
x °
(3a – 40)
°
________________________
________________________
________________________
________________________
________________________
________________________
QUESTION 3
Find the value of the pronumeral, giving reasons.
a
b
c 68°
x °
54°
5 x °
m°
4 x °
________________________
________________________
________________________
________________________
________________________
________________________
Reasoning in geometry Mathletics Instant Workbooks – Series I 2
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2
Reasoning in geometry Topic 3: Angles and the value of pronumerals QUESTION 1
Find the value of the pronumeral in each of the following.
a
b
c
120 130
°
x °
x °
20°
°
x °
15°
25°
________________________
________________________
________________________
________________________
________________________
________________________
d
e
f x °
115°
50°
x °
x °
100°
89
°
________________________
________________________
________________________
________________________
________________________
________________________
QUESTION 2
Find the value of the pronumeral and give reasons for your answer.
a
b
c
x °
36
°
70° 40°
x °
30°
m°
________________________
________________________
________________________
________________________
________________________
________________________
QUESTION 3
Find the value of the pronumeral, giving reasons.
a
b
50
°
a°
60
°
c
x °
p°
65°
35° 20°
________________________
________________________
________________________
________________________
________________________
________________________
d
e
f 140°
30° x °
125°
x °
105
°
40
°
30°
x °
55°
________________________
________________________
________________________
________________________
________________________
________________________
Reasoning in geometry Mathletics Instant Workbooks – Series I 2
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3
Reasoning in geometry Topic 4: Parallel lines and angles QUESTION 1
Find the value of the pronumeral in each of the following.
a
b
c 115°
70°
65°
p°
x °
x °
________________________
________________________
________________________
________________________
________________________
________________________
d
e 69°
f
x °
n°
98°
y °
m°
70°
________________________
________________________
________________________
________________________
________________________
________________________
QUESTION 2
Find the value of the pronumeral, giving reasons.
a
b x °
c x °
140°
66°
87°
m°
________________________
________________________
________________________
________________________
________________________
________________________
QUESTION 3
Find the value of the pronumeral, giving reasons.
a
b
c 130°
2t
°
37
°
x °
110
°
°
y
________________________
________________________
________________________
________________________
________________________
________________________
d
e
f 65° x °
70°
30°
x °
x °
y °
________________________
________________________
________________________
________________________
________________________
________________________
Reasoning in geometry Mathletics Instant Workbooks – Series I 2
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4
Reasoning in geometry Topic 5: Triangles and the value of pronumerals QUESTION 1
Find the value of the pronumeral.
a
b
c
50°
y °
68°
60°
x °
x °
42°
35
°
________________________
________________________
________________________
________________________
________________________
________________________
d
e
y °
f
2 x
°
70°
60°
( x + 20)
°
x °
________________________
________________________
________________________
________________________
________________________
________________________
QUESTION 2
Find the value of the pronumeral.
a
b
c
3 x °
100
°
3a
60°
2a
°
x °
4a
°
2a
°
°
________________________
________________________
________________________
________________________
________________________
________________________
d
e
3a°
f
84
3 x °
°
2a°
x °
________________________
________________________
________________________
________________________
________________________
________________________
QUESTION 3
Find the value of the pronumeral.
a
b
85
c 80°
°
55
°
y °
d
x °
20°
x °
110°
x °
a°
120°
________________________
________________________
________________________
________________________
________________________
________________________
e
120°
f
80°
x °
x °
________________________
________________________
________________________
________________________
________________________
________________________
115
°
m°
Reasoning in geometry Mathletics Instant Workbooks – Series I 2
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Reasoning in geometry Topic 6: Quadrilaterals and the value of pronumerals QUESTION 1
Find the value of the pronumeral.
a
b 63°
c
2 x °
95°
106° 25°
87°
92°
80°
x
°
105°
x °
x
°
________________________
________________________
________________________
________________________
________________________
________________________
d
e
f °
25°
70
x
°
60°
98°
120°
95 °
130
°
20°
y °
75°
x °
________________________
________________________
________________________
________________________
________________________
________________________
QUESTION 2
Find the value of the pronumeral.
a
b
60°
c
70°
3 y °
100°
92°
y ° 80°
80°
b
a
°
°
70°
________________________
________________________
________________________
________________________
________________________
________________________
QUESTION 3
Find the value of the pronumeral.
a
b
c
x ° 75°
70°
3 x
°
220°
x
x
°
230
°
30°
d
2 y °
x °
x °
°
50°
________________________
________________________
________________________
________________________
________________________
________________________
e
120°
f 80°
80°
x
°
120
°
x °
(2 x + 5)
°
y
°
( x – 20)
°
135°
________________________
________________________
________________________
________________________
________________________
________________________
Reasoning in geometry Mathletics Instant Workbooks – Series I 2
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6
Reasoning in geometry Topic 7: Miscellaneous questions QUESTION 1
Find the value of the pronumeral in each of the following.
a
b
c °
°
115°
92
45 x
°
45 110 °
°
y °
75°
( x + 4)
y
y
x °
°
°
x
°
°
________________________
________________________
________________________
________________________
________________________
________________________
d
e
f
y °
40
°
x
°
130°
y
°
40
°
x
°
60
°
________________________
________________________
________________________
________________________
________________________
________________________
QUESTION 2 a
Find the value of the pronumeral in each of the following. 55°
b
45°
c
120 c °
°
b
x x °
°
65
°
48°
a
°
°
x °
50
°
y
°
30
°
________________________
________________________
________________________
________________________
________________________
________________________
QUESTION 3
Find the value of the pronumeral in each of the following.
a
b
c 4 x °
x °
x °
145°
2 x °
________________________
________________________
________________________
________________________
________________________
________________________
d
e 40°
f
38°
65°
y
°
x °
x °
125
°
130
°
30°
________________________
________________________
________________________
________________________
________________________
________________________
Reasoning in geometry Mathletics Instant Workbooks – Series I 2
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7
Reasoning in geometry Topic 8: Deductive geometry QUESTION 1
For the parallelogram shown, prove that
a
+
b
+
c
+
d
= 360°
A
B
a
b
_______________________________________________________________ _______________________________________________________________ _______________________________________________________________ _______________________________________________________________
d
c
D
C
_______________________________________________________________ _______________________________________________________________ QUESTION 2
AB and CD are two intersecting lines. Prove that the vertically opposite angles are equal.
A
D
_______________________________________________________________
b a
_______________________________________________________________
c d
_______________________________________________________________ _______________________________________________________________
C
B
_______________________________________________________________ _______________________________________________________________ QUESTION 3
In the triangle ABC, prove that the exterior angle ACD is equal to the sum of the opposite interior angles a° and b° . In other words, show that ∠ACD = a° + b°
A
a
_______________________________________________________________ _______________________________________________________________ _______________________________________________________________
b
c
B
C
D
C
D
_______________________________________________________________ _______________________________________________________________ _______________________________________________________________ QUESTION 4
A
Prove that the angle sum of a triangle is equal to 180 ° . In other words, show that a° + b° + c ° = 180°
a
_______________________________________________________________ _______________________________________________________________ _______________________________________________________________ _______________________________________________________________
b B
c
_______________________________________________________________ _______________________________________________________________
Reasoning in geometry Mathletics Instant Workbooks – Series I 2
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Reasoning in geometry Topic 9: Problem solving and geometry 1
Two angles of a triangle are 55 ° and 45 ° . Find the third angle. ______________________________________________________________________________________
2
Three angles of a quadrilateral are 80 ° , 60° and 140° . Find the fourth angle. ______________________________________________________________________________________
3
If one of the base angles of an isosceles triangle is 72 ° , find the size of the vertex angle. ______________________________________________________________________________________
4
If the vertex angle of an isosceles triangle is 82 ° , find the size of each of the base angles. ______________________________________________________________________________________
5
If a triangle has all three sides equal, find the size of each angle. ______________________________________________________________________________________
6
In a right-angled triangle the two shorter sides are equal. What is the size of each acute angle? ______________________________________________________________________________________
7
In a right-angled triangle one of the angles is 50 ° . Find the other acute angle. ______________________________________________________________________________________
8
In a rhombus one angle is 120 ° . Find the size of the other angles. ______________________________________________________________________________________
9
The angles of a triangle are x ° , 2 x ° and 3 x ° . Find the size of each angle. ______________________________________________________________________________________ ______________________________________________________________________________________
10 In a parallelogram one of the angles is 65 ° . Find the size of all other angles.
______________________________________________________________________________________ ______________________________________________________________________________________ 11 In a right-angled triangle one acute angle is four times the size of the other acute angle.
What is the size of each angle? ______________________________________________________________________________________ ______________________________________________________________________________________ 12 ABCD is a rectangle. If ∠DBC = 60 ° , find ∠BDC.
A
B 60°
______________________________________________ D
C
______________________________________________
Reasoning in geometry Mathletics Instant Workbooks – Series I 2
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9
Reasoning in geometry Topic Test Instructions
PART A This part consists of 12 multiple-choice questions Each question is worth 1 mark Fill in only ONE CIRCLE for each question Calculators are NOT allowed
Time allowed: 15 minutes
Total marks = 12 Marks
1
The number of sides equal in an equilateral triangle are A
2
none
B
2
C
3
D
none of these
1
none
B
2
C
3
D
none of these
1
90
°
B
180
C
°
270
°
D
360
1
D
360
1
D
none of these
1
D
none of these
1
D
none of these
1
D
none of these
1
D
none of these
1
°
90
°
B
180
C
°
270
°
°
1
B
2
C
3
1
B
2
C
3
1
B
2
C
3
If two angles of a triangle are complementary, then the third angle is A
0
1
The number of right angles in a right-angled triangle: A
9
none of these
The number of obtuse angles in an obtuse-angled triangle: A
8
D
The number of acute angles in an acute-angled triangle: A
7
3
The angle sum of a quadrilateral is always equal to A
6
C
The angle sum of a triangle is always equal to A
5
2
The number of sides equal in a scalene triangle are A
4
B
The number of sides equal in an isosceles triangle are A
3
none
acute
B
right-angled
C
obtuse
In any right-angled triangle, the other two angles are both A
acute
B
right angles
C
obtuse
Reasoning in geometry Mathletics Instant Workbooks – Series I 2
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Reasoning in geometry Topic Test
PART A continued
Marks
eason ng n geome ry
11
In a triangle, the number of right angles can be A
12
C
3
D
none of these
1
scalene
B
°
acute-angled
C
right-angled
D
obtuse-angled
C
4
D
5
C
4
D
5
D
360
1
The minimum number of sides in a polygon: 2
B
3
1
The number of sides in a quadrilateral: A
15
2 °
A
14
B
In a triangle, if one angle is 38 and the other is 52 , the triangle is called A
13
1
2
B
3
1
The sum of the exterior angles of any polygon is equal to A
90
°
B
180
°
C
270
°
°
Total marks achieved for PART A
Reasoning in geometry Mathletics Instant Workbooks – Series I
Copyright © 3P Learning
1
15
11
Reasoning in geometry Topic Test
PART B
Instructions
This part consists of 15 questions Each question is worth 1 mark Write answers in the answers-only column
Time allowed: 20 minutes
Total marks = 15
Questions
Answers only
Marks
Name the following angles. 1
2
3
___________________
1
___________________
1
___________________
1
Find the value of the pronumeral. 4
5
6
___________________ 110
°
58°
115°
x °
72
°
x °
___________________ ___________________
x °
1 1 1
7
8
9
x °
72°
135°
___________________ 1
125
°
x °
___________________ 1
x °
56°
___________________
83
°
1
10
11
12
___________________
p°
50°
m°
a°
1
70°
___________________ 1
65°
48
°
___________________ 1
13
14
15
75°
___________________
45
°
x °
1 y °
3 x
°
35
°
68°
x ° x °
x °
92°
___________________ 1
___________________ 1
Total marks achieved for PART B Reasoning in geometry Mathletics Instant Workbooks – Series I 2
Copyright © 3P Learning
15
12
Reasoning in geometry Topic Test
PART C
Instructions
This part consists of 4 questions Each question is worth 5 marks Show all necessary
Time allowed: 20 minutes
Total marks = 20 Marks
Questions 1
2
Comlete the following statements. a
The base angles of an isosceles triangle are _________________ .
b
The size of each interior angle of an equilateral triangle is ________________ .
c
A right angle is equal to _________________ .
d
A quadrilateral is a________________ sided plane figure.
e
A trapezium is a quadrilateral in which one pair of opposite sides are _________________ .
5
Find the value of the pronumeral in each of the following. a
b
c 110°
120
°
x °
a°
2 x
°
x °
___________________ d
___________________
___________________
e 60°
20°
3a°
x °
___________________ 3
___________________
5
Find the value of each pronumeral, giving reasons. a
b
y °
c
60°
(2 x + 30)
°
y ° x °
4
60
°
150
°
x °
___________________
___________________
___________________
___________________
___________________
___________________
5
Find the value of each pronumeral, giving reasons. a
a°
148
°
72
°
b
( x + 10) y °
63
°
°
c
100
°
110
°
40
°
x °
y °
___________________
___________________
___________________
___________________
___________________
___________________
Total marks achieved for PART C Reasoning in geometry Mathletics Instant Workbooks – Series I
Copyright © 3P Learning
5
20
13
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