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NCERT Solutions for Class 7 Maths Chapter 7 - Congruence of triangles is one of the important topics of the geometry. In this chapter, there are two exercises and topic wise practice questions. The solutions of NCERT Class 7 chapter 7 congruence of triangles give detailed explanations to all these questions. Students can do their homework easily if they have a tool like NCERT Solutions for Class 7 in hand. In geometry, two objects or two figures are congruent if they have the same dimension and same shape, or in other words, we can say that two objects or figures are congruent if both are exact copies of one another. The relation of two objects or two figures being congruent is called congruence.
NCERT Chapter 7 Maths c 7 congruence of triangles deal with plane figures or 2D only, although congruence is a general concept applicable to 3D figures also. Congruence of plane figures, congruence among line segments, congruence of angles, congruence of triangles, some criteria for congruence of triangles like SSS congruence of two triangles, SAS congruence of two triangles, ASA congruence of two triangles, RHS congruence of two right-angled triangles are the concepts which are covered in this chapter. Questions on all these concepts are discussed in the NCERT solutions for Class 7 Maths chapter 7 congruence of triangles. The NCERT Solutions are prepared in such a manner that students are able to understand the concepts easily and prepare themselves very well for CBSE final exams to score higher marks. Here you will get solutions to two exercises in NCERT .
Criteria for Congruence of Triangles:
Congruence of Lines: Two lines are congruent if they have the same length.
Congruence of Angles: Two angles are congruent if they have the same measure.
Congruence of Triangles: Two triangles are congruent if they are exact copies of each other and cover each other completely when superposed.
Criteria for Congruence of Triangles:
Free download NCERT Solutions for Class 7 Maths Chapter 7 Congruence of Triangles PDF for CBSE Exam.
Answer:
the other four correspondences by using two cutouts of triangles are :
Answer:
i) Since
AB = PQ
BC = QR
CA = PR
So, by SSS congruency rule both triangles are congruent to each other.
ii) Since,
ED = MN
DF = NL
FE = LM
So, by SSS congruency rule both triangles are congruent to each other.
.
iii) Since
AC = PR
BC = QR But
So the given triangles are not congruent.
iv) Since,
AD = AD
AB = AC
BD = CD
So, By SSS Congruency rule, they both are congruent to each other.
.
2. In Fig 7.15, and D is the mid-point of .
(i) State the three pairs of equal parts in and
(ii) Is Give reasons.
(iii) Is Why?
Answer:
Here in and
i) Three pair of equal parts are:
AD = AD ( common side )
BD = CD ( as d is the mid point of BC)
AB = AC (given in the question)
ii) Now,
by SSS Congruency rule,
iii) As both triangles are congruent to each other we can compare them and say
.
3. In Fig 7.16, and . Which of the following statements is meaningfully written?
Answer:
Given,
and
.
AB = AB ( common side )
So By SSS congruency rule,
.
So this statement is meaningfully written as all given criterions are satisfied in this.
Answer:
Here, in .
i)the three pairs of equal parts in are
AB = AC
BC = CB
AC = AB
ii)
Hence By SSS Congruency rule, they both are congruent.
iii) Yes, because are congruent and by equating the corresponding parts of the triangles we get,
.
1. Which angle is included between the sides and of ?
Answer:
Since both the sides and intersects at E,
is included between the sides and of .
Answer:
To prove congruency by SAS rule, we need to equate two corresponding sides and one corresponding angle,
so in proving we need,
And
.
Hence the extra information we need is .
Answer:
i) in and
AB = DE
AC = DF
Hence, they are not congruent.
ii) In and
AC = RP = 2.5 cm
CB = PQ = 3 cm
Hence by SAS congruency rule, they are congruent.
.
iii) In and
DF= PQ = 3.5 cm
FE= QR = 3 cm
Hence, by SAS congruency rule, they are congruent.
iv) In and
QP = SR = 3.5 cm
PR = RP (Common side)
Hence, by SAS congruency rule, they are congruent.
.
1. What is the side included between the angles and N of ?
Answer:
The side MN is the side which is included between the angles and N of .
Answer:
As we know, in ASA congruency two angles and one side is equated to their corresponding parts. So
To Prove
And The side joining these angles is
.
So the information that is needed in order to prove congruency is .
4. In Fig 7.25, and bisect each other at .
(i) State the three pairs of equal parts in two triangles and .
(ii) Which of the following statements are true?
Answer:
i) The three pairs of equal parts in two triangles and are:
CO = DO (given)
OA = OB (given )
( As opposite angles are equal when two lines intersect.)
ii) So by SAS congruency rule,
that is
Hence, option B is correct.
Answer:
i) in and
AB = FE = 3.5 cm
So by ASA congruency rule, both triangles are congruent.i.e.
ii) in and
But,
So, given triangles are not congruent.
iii) in and
RQ = LN = 6 cm
So by ASA congruency rule, both triangles are congruent.i.e.
.
iv) in and
AB = BA (common side)
So by ASA congruency rule, both triangles are congruent.i.e.
Answer:
i)
Given in and .
So, by ASA congruency criterion, they are congruent to each other.i.e.
.
ii)
Given in and .
For congruency by ASA criterion, we need to be sure of equity of the side which is joining the two angles which are equal to their corresponding parts. Here the side QR is not given which is why we cannot conclude the congruency of both the triangles.
iii)
Given in and .
For congruency by ASA criterion, we need to be sure of equity of the side which is joining the two angles which are equal to their corresponding parts. Here the side QR is not given which is why we cannot conclude the congruency of both the triangles.
5. In Fig 7.28, ray AZ bisects as well as .
(i) State the three pairs of equal parts in triangles and .
(ii) Is Give reasons.
(iii) Is Justify your answer.
(iv) Is Give reasons.
Answer:
i)
Given in triangles and
( common side)
ii)
So, By ASA congruency criterion,triangles and are congruent.
iii)
Since , all corresponding parts will be equal. So
.
iv)
Since , all corresponding parts will be equal. So
Answer:
i) In and
Hence they are not congruent.
ii)
In and
( same side )
So, by RHS congruency rule,
iii)
In and
( same side )
So, by RHS congruency rule,
iv)
In and
( same side )
So, by RHS congruency rule,
and
Answer:
To prove congruency by RHS (Right angle, Hypotenuse, Side ) rule, we need hypotenuse and side equal to the corresponding hypotenuse and side of different angle.
So Given
( Right angle )
( Side )
So the third information we need is the equality of Hypotenuse of both triangles. i.e.
Hence, if this information is given then we can say,
.
3. In Fig 7.33, and are altitudes of such that .
(i) State the three pairs of equal parts in and .
(ii) Is ? Why or why not?
(iii) Is ? Why or why not?
Answer:
i) Given, in and .
ii) So, By RHS Rule of congruency, we conclude:
iii) Since both the triangle are congruent, all parts of one triangle are equal to their corresponding part from another triangle.
So.
.
4. ABC is an isosceles triangle with and is one of its altitudes (Fig 7.34).
(i) State the three pairs of equal parts in and .
(ii) Is ? Why or why not?
(iii) Is ? Why or why not?
(iv) Is ? Why or why not?
Answer:
i) Given in and .
( Common side)
ii) So, by RHS Rule of congruency, we conclude
iii) Since both triangles are congruent all the corresponding parts will be equal.
So,
iv) Since both triangles are congruent all the corresponding parts will be equal.
So,
.
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 ___________.
Answer:
a) Two line segments are congruent if they are identical in shape and size and which is the case when the length of two line segments are equal.
b) As the congruent things are a photocopy of each other.
c) When we write , We mean that both the angles(A & B) are equal.
2. Give any two real-life examples for congruent shapes.
Answer:
Any two things that have identical shape and size are congruent like all the same kind of pens are congruent to one another. every same kind of bench in class are congruent to one another.all the similar football is congruent to one another.
3. If under the correspondence write all the corresponding congruent parts of the triangles.
Answer:
Corresponding parts of the two congruent triangles are :
Sides:
Angles:
1.(a) Which congruence criterion do you use in the following?
Answer:
Since we are comparing all the sides of two triangles, The SSS (side, side, side) Congruent criterion is used.
1.(b) Which congruence criterion do you use in the following?
Answer:
Since we are comparing two sides and one angle of the two triangles, the SAS (sie, angle, side) congruent criterion is used to prove them congruent.
1.(c) Which congruence criterion do you use in the following?
Answer:
Since we are comparing two angles and one side, ASA(Angle, Side, Angle) congruency criterion is used to prove the congruency.
1.(d) Which congruence criterion do you use in the following?
Answer:
Since we are comparing two sides and one angle of the two triangles, the SSA (Side, Side, Angle) congruent criterion is used to prove the congruency.
2.(a) You want to show that
(a) If you have to use criterion, then you need to show
Answer:
As we know that in the criterion of proving congruent, all three corresponding sides are equal to another. So to prove the congruency, we kneed to know the following things:
2.(b) You want to show that
(b) If it is given that and you are to use SAS criterion, you need to have
Answer:
As we know in SAS criterion the two sides and one angle are identical to their corresponding parts of another triangle. So to prove congruency we need to prove that,
2.(c) You want to show that
(c) If it is given that and you are to use ASA criterion, you need to have
Answer:
Given,
also,
Now, As we know in the ASA criterion of proving congruency, the one and side two angles are equal to their corresponding parts. So,
3. You have to show that . In the following proof, supply the missing reasons.
Answer
Steps | Reasons |
Given in the question | |
Given in the question. | |
the side which is common in both triangle | |
By SAS Congruence Rule |
4. In , , and .
In , , and . A student says that by AAA congruence criterion. Is he justified? Why or why not?
Answer:
No, because it is not necessary that two triangles will be congruent if their all three corresponding angles are equal. in this case, the triangles might be zoomed copy of one another.
5. In the figure, the two triangles are congruent. The corresponding parts are marked. We can write ?
Answer:
Comparing from the figure.
By SAS Congruency criterion, we can say that
]
6. Complete the congruence statement:
Answer:
Comparing from the figure, we get,
So By SSS Congruency Rule,
Also,
Comparing from the figure, we get,
So By SSS Congruency Rule,
.
What can you say about their perimeters?
Answer:
When two triangles are congruent, the corresponding parts are exactly identical so they have the same area and perimeter.
While the triangles are not congruent but have the same area, then the perimeter of both triangles are not equal.
Answer:
Five pairs of congruent parts can be three pairs of sides and two pairs of angles. In that case, the SAS or ASA criterion would prove them to be congruent. Hence, such a figure is not possible.
Answer:
Given
One additional pair which is not given in the figure is
We used the ASA Criterion as the two corresponding angles are given and we figured out the side by congruency.
Chapter No. | Chapter Name |
Chapter 1 | |
Chapter 2 | |
Chapter 3 | |
Chapter 4 | |
Chapter 5 | |
Chapter 6 | |
Chapter 7 | Congruence of Triangles |
Chapter 8 | |
Chapter 9 | |
Chapter 10 | |
Chapter 11 | |
Chapter 12 | |
Chapter 13 | |
Chapter 14 | |
Chapter 15 |
The same questions described in the NCERT solutions for Class 7 Maths chapter 7 Congruence of Triangles can be expected for exams.
Also Check NCERT Books and NCERT Syllabus here:
Yes, the chapter is important for higher studies in the field of maths and science and also in class 8, 9 and 10 maths also. Therefore practice congruence of triangles class 7 pdf which can be downloaded form the link given above in this article.
The objects having the same shape and the same size are called congruent object. To know more in detail students can study class 7 maths chapter 7 pdf.
There are 2 exercises in NCERT solution Class 7 Maths Chapter 7
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