A tale of 3 intersecting lines worksheet /7th class Maths ganita prakash/prepared by sandeep swamy

A tale of 3 intersecting lines worksheet /7th class Maths ganita prakash/prepared by sandeep swamy/Samyans eduhub

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A tail of 3 intersecting lines
CLASS 07 - MATHS (NEW)
Section A
1)GivenAB= 5cm,̸A= 60
◦
, AC= 4cm . Which
method is used to construct triangle ABC?[1]
a) ASA b) AAA
c) SAS d) SSS
2)When constructing a triangle using a compass and ruler,
what ensures the correct third vertex?[1]
a)Drawing three lines
b)Measuring with a protractor
c)Drawing only circles
d)Intersecting arcs from the ends of the base
3)In which triangle is one side also an altitude?[1]
a) Right - angled b) Isosceles
c) Equilateral d) Scalene
4)To construct a triangle with two sides and the included
angle, what is the correct order?[1]
a)Draw the angle first
b)Draw both sides first, then angle
c)Draw the third side first
d)Draw the base, construct the angle, then mark the
side
5)Which of the following is true for an equilateral triangle?
[1]
a)All sides and all angles are equal
b)All sides are of different lengths
c)Only two sides are equal
d)One angle is90
◦
6)What is the measure of each angle in an equilateral
triangle?[1]
a)90
◦
b)60
◦
c)120
◦
d)45
◦
7)To construct a triangle with sides4cm,5cm , and 6 cm,
which should be drawn first?[1]
a)The side not included between the angles
b)The shortest side
c)Any of the sides
d)The longest side
8)If two angles and their included side are given, which
construction rule applies?[1]
a) SSS b) SSA
c) AAA d) ASA
9)Which tool is essential to construct an equilateral triangle
accurately?[1]
a) Protractor only b) Divider only
c) Compass and ruler d) Set square only
10)If a triangle has side lengths 3 cm, 4 cm and 8 cm,
what can we say?[1]
a)It violates the triangle inequality
b)It is a right triangle
c)It is an equilateral triangle
d)It can be constructed
11)Which tool helps in accurately drawing an altitude?[1]
a) Set square b) Protractor
c) Divider d) Compass
12)When constructing a triangle with two angles(50
◦
,60
◦
)
and included side 5 cm, what is the third angle?[1]
a)70
◦
b)60
◦
c)80
◦
d)90
◦
13)A triangle has all three sides of 5 cm. Which type of
triangle is it?[1]
a) Scalene b) Equilateral
c) Right - angled d) Isosceles
14)What is an altitude in a triangle?[1]
a)A median from the vertex
b)A bisector of an angle
c)A perpendicular from a vertex to the opposite side
d)A line joining midpoints
15)In a triangle with angles50
◦
,60
◦
, and70
◦
, what is the
type based on angles?[1]
a) Equilateral b) Obtuse - angled
c) Acute - angled d) Right - angled
16)Which triangle can never be an equilateral triangle?[1]
a)Triangle with all equal sides
b)Triangle with one90
◦
angle
c)Triangle with all angles60
◦
d)Triangle with equal angles
17)Which condition must be satisfied to construct a triangle
from three given side lengths?[1]
a) Parallel postulate b) Area formula
c) Pythagorean theorem d) Triangle inequality
18)Which triangle has all sides of different lengths?[1]
a) Equilateral b) Right - angled
c) Scalene d) Isosceles
19)Which of the following sets can form an isosceles trian-
gle?[1]
a)5cm,5cm,8cm
b)4cm,4cm,4cm
c)3cm,4cm,5cm
d)2cm,3cm,6cm
20)To construct the altitude from vertex A to side BC, what
is the first step?[1]
a)Mark the midpoint of BC
b)Extend side AC
c)Place set square on BC and draw perpendicular from
A
d)Draw angle bisector
Section B
21)Assertion (A):A triangle cannot be constructed if the
given angles are 100° and 90°.
Reason (R):The sum of angles in any triangle must be
180°.[1]
a)Both A and R are true and R is the correct expla-
nation of A.

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b)Both A and R are true but R is not the correct
explanation of A.
c)A is true but R is false.
d)A is false but R is true.
22)Assertion (A):A triangle can have a side that is also its
altitude.
Reason (R):This happens when the triangle is right -
angled.[1]
a)Both A and R are true and R is the correct expla-
nation of A.
b)Both A and R are true but R is not the correct
explanation of A.
c)A is true but R is false.
d)A is false but R is true.
23)Assertion (A):All angles in an equilateral triangle are
equal.
Reason (R):In an equilateral triangle, all sides are equal.
[1]
a)Both A and R are true and R is the correct expla-
nation of A.
b)Both A and R are true but R is not the correct
explanation of A.
c)A is true but R is false.
d)A is false but R is true.
24)Assertion (A):A triangle with sides 5 cm, 5 cm, and 5
cm is called isosceles.
Reason (R):An isosceles triangle has two equal sides.[1]
a)Both A and R are true and R is the correct expla-
nation of A.
b)Both A and R are true but R is not the correct
explanation of A.
c)A is true but R is false.
d)A is false but R is true.
25)Assertion:An equilateral triangle has one angle of 90°.
Reason:All angles in an equilateral triangle are right an-
gles.[1]
a)Both A and R are true and R is the correct expla-
nation of A.
b)Both A and R are true but R is not the correct
explanation of A.
c)A is true but R is false.
d)A is false but R is true.
Section C
26)Fill in the blanks:[10]
(a)If the two given angles of a triangle are 60° and
50°, the third angle must bedegrees.[1]
(b)A triangle that has one right angle is called a
triangle.[1]
(c)In an equilateral triangle, all the three sides are of
length.[1]
(d)The instrument commonly used to construct a precise
altitude is the.[1]
(e)A triangle with side lengths 3 cm, 4 cm, and 5 cm
is a triangle.[1]
(f)To construct a triangle when its three sides are given,
we draw arcs from the ends of the base using a
compass so that they at the third vertex.[1]
(g)In a triangle, the sum of all interior angles is always
.[1]
(h)When two sides and the angle between them are
given, the construction method is called the
criterion.[1]
(i)In an equilateral triangle, all sides are equal and
each interior angle measuresdegrees.[1]
(j)To construct an equilateral triangle with side 4 cm,
we draw arcs of radius 4 cm from both endpoints
of the base using a.[1]
Section D
27)Check whether a triangle can be formed with the side
lengths 1, 100, and 100.[1]
28)Name the triangle construction rule used when two sides
and the included angle are known.[1]
29)Check whether a triangle can be formed with the side
lengths 5, 10, 12[1]
30)What tool is mainly used to draw arcs while constructing
a triangle with given sides?[1]
31)What is an altitude in a triangle?[1]
32)What type of triangle has all angles less than 90
o
?[1]
33)A triangle has sides 5 cm, 5 cm, and 8 cm. What type
of triangle is this?[1]
34)Check whether a triangle can be formed with the side
lengths 1, 1, 5[1]
35)Which instrument is commonly used to construct an alti-
tude accurately?[1]
36)What happens when the three vertices lie on a straight
line?[1]
37)Construct a triangle for the following measurements:
75°, 5 cm, 75°[2]
38)What kind of triangle is formed if all three sides are
different and all angles are acute?[2]
39)What is an altitude of a triangle? How can you draw it
using a set square?[2]
40)What is the triangle inequality rule? Give an example
showing when a triangle is not possible.[2]
41)How can you identify whether a triangle is right - angled
using side lengths?[2]
42)Classify the triangle with sides 6 cm, 6 cm, and 4 cm
by its sides and angles.[2]
43)Describe the steps to construct a triangle withAB=
6cm,̸A= 60
◦
, andAC= 5cm.[2]
44)Draw the given angles and construct their angle bisec-
tor.C 108°D 140°[2]
45)Construct triangle for the following measurements:
120°, 6 cm, 30°[2]
46)Can a triangle be constructed with angles 100
o
and 90
o
?
Justify your answer.[2]
47)Explain the step - by - step method to construct a triangle
with sides 3 cm, 4 cm, and 5 cm.[3]
48)A triangle has angles30
◦
,60
◦
, and90
◦
. Classify it by
both angles and sides.[3]
49)Find the third angle of a triangle (using a parallel line)
when two of the angles are 36°, 72°[3]
50)Describe how to check if a triangle with sides 4 cm, 6
cm, and 10 cm is possible. If yes, construct it.[3]
51)Construct a triangle with side lengths 1 cm, 5 cm, and
5 cm.[3]
52)Construct an equilateral triangle with each side measuring
3.5 cm, 3.5 cm, 3.5 cm[3]
53)Find the third angle of a triangle (using a parallel line)
when two of the angles are 150°, 15°[3]

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54)Construct a triangle with side lengths 4 cm, 6 cm, and
8 cm.[3]
55)How do you construct an equilateral triangle of side 5
cm using only a compass and ruler? Explain each step
clearly.[3]
56)Define an equilateral triangle. Explain its properties and
construct an equilateral triangle with each side measuring
6 cm.[5]
57)What is an altitude in a triangle? Draw and label the
altitudes of an acute triangle.[5]
Section E
58)Read the following text carefully and answer the questions
that follow:
Ragini wanted to create different triangle shapes for her
project using paper strips of various lengths. She picked
three strips of lengths 3 cm, 4 cm, and 8 cm. Despite
trying multiple times, she couldn’t join them to form a
triangle. Her teacher explained to her about the triangle
inequality and helped her explore which combinations of
lengths can form valid triangles.Questions:
i.Why was Ragini unable to form a triangle using
strips of lengths 3 cm, 4 cm, and 8 cm?(1)
ii.What is the Triangle Inequality Theorem?(1)
iii.Ragini wanted to use paper strips of lengths 6 cm,
7 cm, and 12 cm to form a triangle. Can she do
so? Justify your answer using the Triangle Inequal-
ity Theorem.(2)
OR
After learning the Triangle Inequality Theorem,
Ragini tested strips of lengths 5 cm, 9 cm, and
14 cm. Could she form a triangle? Explain your
answer.(2)
[4]
59)Read the following text carefully and answer the questions
that follow:
Kanishka was working on a geometry project and wanted
to draw a triangle with one of its sides, AB, measuring 5
cm. She knew the measures of two angles:̸A = 60°
and̸B = 70°. Before beginning the construction, she
decided to calculate the third angle,̸C, to ensure the
triangle would be valid. Using the angle sum property
of triangles, she found that̸C = 180° - (60° + 70°)
= 50°. This confirmed that the triangle could be drawn.
While doing so, Kanishka wondered if it was possible to
form a triangle when the sum of any two angles exceeds
180°, and she learned that such a triangle is not possi-
ble as the total angle sum must always be exactly 180°.
Questions:
i.Kanishka wanted to find the third angle of a triangle
with̸A = 60° and̸B = 70°. What will be the
measure of̸C?(1)
ii.Can a triangle exist if the sum of any two angles
is more than 180°? Why or why not?(1)
iii.Kanishka planned to draw a triangle with AB = 5
cm,̸A = 60°, and̸B = 70°. Before construction,
she calculated̸C. Explain why this step is im-
portant and how it helps in constructing the triangle
accurately.(2)
OR
Explain why a triangle cannot be formed if the sum
of two given angles is already more than 180°, using
an example. How did this concept help Kanishka
clarify her doubt?(2)
[4]