NCERT Maths Solution for Class 7 Chapter 7 Congruence of triangles:
In this chapter of Class 7 Maths Chapter 7, we learn the congruence criterion of triangle. Like SSS, SAS, ASA and Right angle triangle congruence.
The student can download the solution in pdf format for free of cost. In this section we discuss about following topics. You can direct access the topic from the given link.
Solution Exercise 7.1
Solution Exercise 7.2
Download the pdf of Exercise 7.1 and Exercise 7.2
Definitions and important facts
Class 7 Maths Chapter 7 Solution Exercise 7.1
Question 1:
Complete the following statements:
(a) Two line segments are congruent if _________.
(b) Among two congruent angles, one has a measure of 70°; the measure of
the other angle is _________.
(c) When we write ∠A = ∠B, we actually mean _________.
Answer 1:
(a) They have same length.
(b) 70º
(c) n ∠A = n ∠B
Question 2:
Give any two real-life examples for congruent shapes.
Answer 2:
(i) Coin of same denomination of same modal and (ii) Biscuits of same packet.
Question 3:
If ΔABC ≅ ΔFED under the correspondence ABC ↔ FED, write all the corresponding congruent parts of the triangles.
Answer 3:
∠A ↔ ∠F, ∠B ↔ ∠E, ∠C ↔ ∠D, AB ↔ FE, BC ↔ ED, CA ↔ DF
Question 4:
If ΔDEF ≅ ΔBCA, write the part(s) of ΔBCA that correspond to
(i) ∠E (ii) EF (iii) ∠F (iv) DF
Answer 4:
(i) ∠E ↔ ∠C, (ii) EF ↔ CA (iii) ∠F ↔ ∠A, (iv) DF ↔ BA
Class 7 Maths Chapter 7 Exercise 7.2 Solution
Question 1:
Which congruence criterion do you use in the following?
(a) Given: AC = DF
AB = DE
BC = EF
So, ΔABC ≅ ΔDEF
(b) Given: ZX = RP
RQ = ZY
∠PRQ = ∠XZY
So, ΔPQR ≅ ΔXYZ
(c) Given: ∠MLN = ∠FGH
∠NML = ∠GFH
ML = FG
So, ΔLMN ≅ ΔGFH
(d) Given: EB = DB
AE = BC
∠A = ∠C = 90°
So, ΔABE ≅ ΔCDB
Answer 1:
(a) By SSS Congruence criterion.
(b) By SAS Congruence criterion.
(c) By ASA Congruence criterion
(d) RHS, as in the given two right –angled triangles, one side and the hypotenuse are respectively equal.
Question 2:
You want to show that ΔART ≅ ΔPEN,
(a) If you have to use SSS criterion, then you need to show
(i) AR = (ii) RT = (iii) AT =
(b) If it is given that ∠T = ∠N and you are to use SAS criterion, you need to have
(i) RT = and (ii) PN =
(c) If it is given that AT = PN and you are to use ASA criterion, you need to have
(i) ? (ii) ?
Answer 2:
(a) (i) AR = PE (ii) RT = EN (iii) AT = PN
(ii) (i) RT = EN and (ii) PN = AT
(iii) (i) ∠PNE = ∠ATR (ii) ∠EPN = ∠RAT
Question 3:
You have to show that ΔAMP ≅ ΔAMQ. In the following proof, supply the missing reasons.
Answer 3:
(i) Given
(ii) Given
(iii) Common side
(iv) By SAS congruence criterion
Question 4:
In ΔABC, ∠A = 30° , ∠B = 40° and ∠C = 110° In ΔPQR, ∠P = 30° , ∠Q = 40° and ∠R = 110° A student says that ΔABC ≅ ΔPQR by AAA congruence criterion. Is he justified? Why or why not?
Answer 4:
No, because this property represents that these triangles have their respective angles of equal measure. But, this gives us no information about their side’s length.
Question 5:
In the figure, the two triangles are congruent. The corresponding parts are marked. We can write ΔRAT ≅ ?
Answer 5:
From given Fig. it is seen that, AR = OW, AT = ON and ∠A= ∠O Therefore ΔRAT ≅ ΔWON, by SAS congruence criterion. We can also show it by SSS congruence criterion.
Question 6:
Complete the congruence statement:
Answer 6:
In Fig. (i)
BT = BC (Given)
CA = TA (Given)
and BA = BA (Common), So, ΔBCA ≅ ΔBTA , By SSS congruence criterion.
In Fig. (ii)
PQ = RS (Given)
TQ = QS (Given)
and PT = QR , Therefore ΔQRS ≅ ΔQPT, By SSS Congruence criterion.
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?
Answer 7:
Here Δ ABC and Δ PQR are congruent and have the same area. The perimeter of the both triangle also same.
There are two triangle of same height and same base . Therefore their area are same, But they are not congruent. And perimeter of both triangle are not equal. Δ XYZ and Δ I JK
Question 8:
If ΔABC and ΔPQR are to be congruent, name one additional pair of corresponding parts. What criterion did you use?
Answer 8:
In ΔABC and ΔPQR , the additional pair is BC = QR
∠B = ∠Q = 90° (Given)
∠C = ∠R, Therefore ΔABC ≅ ΔPQR , By ASA congruence criterion.
Question 9:
Explain, why ΔABC ≅ ΔFED.
Answer 9:
In given Fig. BC = DE (Given)
∠B = ∠E (Given)
∠A = ∠F (Given)
Therefore ΔABC ≅ ΔFED , By ASA Congruence criterion.
Definition and Important fact:
Congruence : If we have two object, which is exact copy of one another, then they are called congruence.
In other word , if the two objects are same size and same shape ,and if we put one object to another and it covers completely, then the objects is called congruence.
For example , Shaving blade of the same company, Biscuits in the same packet. Coins of same denomination etc.
Congruence of Plane Figures: In our daily life we can see many plane of papers are congruent. Means if we place one of then over the other then it covers each other completely.
Then they are congruence. For example: If we take two books of NCERT Maths Class 7 and place one over other, Then it covers completely each other. And they seen looks alike, which means they are congruent.
Congruence Among Line Segments: If we draw two line segments of the same length and same width. And if we plaece one over the other then the line segment coincide to each other. Then the line segments are congruent.
Note: If two line segments have the same (i.e., equal) length, they are congruent. Also, if two line segments are congruent, they have the same length.
Conruence of Angle : If we trace an angle 30 degree,second angle of 40degree and third angle of 30 degree.
Now if we superpose 30 degree angle (first angle) over the angle 40 degree (second angle), then they are not exactely matches.
Therefore angle 30 degree (first angle) and angle 40 degree (second angle) are not congruent. And now we superpose the angle 30 degree (first angle) over the angle 30 degree (third angle), then they exact cover to each other.
Therefore the angle 30 degree (First angle)and angle 30 degree (third angle) are congruent.
Notes: If two angles have the same measure, they are congruent. Also, if two angles are congruent, their measures are same.
Congruence of Triangles : We saw that two line segments are congruent where one of them, is just a copy of the other.
Similarly, two angles are congruent if one of them is a copy of the other. Two triangles are congruent if they are copies of each other and when placed one over to other , they cover each other completely.
Congruence:
In NCERT Class 7 Maths Chapter 7 ,there are 4 types of congruence. Which is given below.
SSS Congruence criterion: If we draw two triangle of the same length. Which have all sides equal. Let a triangle ABC length of each sides is 4cm and other triangle PQR , which have all sides measured 4cm.
Then the both triangle are congruent. Because here sises of both triangles are equal Therefore here SSS Cogruence criterion applied .
Note: If under a given correspondence, the three sides of one triangle are equal to the three corresponding sides of another triangle, then the triangles are congruent.
SAS Congruence criterion:
If under a correspondence, two sides and the angle included between them of a triangle
are equal to two corresponding sides and the angle included between them of another
triangle, then the triangles are congruent.
ASA Congruence criterion:
If under a correspondence, two angles and the included side of a triangle are equal to
two corresponding angles and the included side of another triangle, then the triangles
are congruent.
RHS Congruence criterion:
If under a correspondence, the hypotenuse and one side of a right-angled triangle are
respectively equal to the hypotenuse and one side of another right-angled triangle, then
the triangles are congruent.