Chapter
7: Congruence
of Triangles
Exercise: 7.1 (4)
Question: 1
Complete the following statements:
a.
Two line segments are congruent
if __________.
b.
Among two congruent angles, one
has a measure of ;
the measure of the other angle is _________.
c.
When we write , we actually mean
___________.
Solution
a.
They have the same length
b.
c.
Question: 2
Give any two real-life examples for congruent shapes.
Solution
(i)
Two footballs
(ii)
Pages of same book
Question: 3
If under the
correspondence write all the
corresponding congruent parts of the triangles.
Solution
Given:
The corresponding congruent parts of the triangles are:
(i)
(ii)
(iii)
(iv)
(v)
(vi)
Question: 4
If , write the part(s) of that correspond to
(i)
(ii)
(iii)
(iv)
Solution
Given: .
(i)
(ii)
(iii)
(iv)
Exercise: 7.2 (10)
Question: 1
Which congruence criterion do you use in the
following?
a. Given :
So,
b.
Given:
So,
c.
Given:
So,
d.
Given:
So,
Solution
a.
By congruence criterion,
since it is
given that
The three sides
of one triangle are equal to the three corresponding sides of another triangle.
Therefore,
b.
By congruence criterion,
since it is given that and
The two sides
and one angle in one of the triangle are equal to the corresponding sides and
the angle of other triangle.
Therefore,
c.
By congruence criterion,
since it is
given that
The two angles
and one side in one of the triangle are equal to the corresponding angles and
side of other triangle.
Therefore,
d.
By congruence criterion,
since it is given that
Hypotenuse and one side of a
right angled triangle are respectively equal to the hypotenuse and one side of
another right angled triangle.
Therefore,
Question:
2
You want to show that
a. If you have to use criterion, then you need to show
(i)
(ii)
(iii)
b. If it is given that and you
are to use SAS criterion, you need to have
(i)
and
(ii)
c. If it is given that and
you are to use ASA criterion, you need to have
(i)
(ii)
Solution
a.
Using SSS criterion,
(i)
(ii)
(iii)
b.
Given:
Using SAS
criterion,
(i)
(ii)
c.
Given:
Using ASA
criterion,
(i)
(ii)
Question:
3
You have to show that . In the following proof, supply the missing reasons.
Steps
|
Reasons
|
(i)
|
(i) ………….
|
(ii)
|
(ii) ………….
|
(iii)
|
(iii) ………….
|
(iv)
|
(iv) ………….
|
Solution
Steps
|
Reasons
|
(i)
|
(i) Given
|
(ii)
|
(ii) Given
|
(iii)
|
(iii) Common
|
(iv)
|
(iv) congruence rule
|
Question:
4
In ,
and .
In ,
and .
A student says that by
congruence
criterion. Is he justified? Why or why not?
Solution
No, because the two triangles with equal corresponding angles
need not be congruent. In such a correspondence, one of them can be an enlarged
copy of the other.
Question:
5
In the figure, the two triangles are congruent. The
corresponding parts are marked. We can write
Solution
In the figure, given two triangles are congruent. So, the
corresponding parts are:
, , ,
We can write,
[By
congruence rule]
Question: 6
Complete the congruence statement:
Solution
In and , given triangles are congruent so the corresponding
parts are:
, , ,
Thus,
[By congruence rule]
In and , given triangles are congruent so the corresponding parts
are:
, , ,
Thus,
[By congruence rule]
Question:
7
In a squared sheet, draw two triangles of
equal areas such that
(i)
the triangles are congruent.
(ii)
the triangles are not congruent.
What can you say about their perimeters?
Solution
In a squared sheet, draw and .
When two triangles have equal areas and
(i)
these triangles are congruent, i.e., [By congruence rule]
Then, their
perimeters are same because length of sides of first triangle are equal to the
length of sides of another triangle by congruence rule.
(ii)
But, if the triangles are not congruent, then
their perimeters are not same because lengths of sides of first triangle are
not equal to the length of corresponding sides of another triangle.
Question:
8
Draw a rough sketch of two triangles such that they have five pairs of
congruent parts but still the triangles are not congruent.
Solution
Let us draw two triangles and .
All angles are equal, two
sides are equal except one side. Hence, are not congruent to .
Question:
9
If and are to be congruent, name one additional pair
of corresponding parts. What criterion did you use?
Solution
and are
congruent. Then one additional pair is
Given:
Therefore,
[By
congruence rule]
Question: 10
Explain,
why
Solution
Given:
In and
[Given]
Using angle sum property in both triangles and we find that
Also, [Given]
Therefore,
[By congruence rule]