## NCERT Solutions for class 7 Maths Chapter 7: Congruence of Triangles## Exercise 7.1
(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
∠A = ∠B means that the value or the measure of the two angles are equal. If the measure of ∠A is 50°, the measure of ∠B is also equal to 50°.
The real examples for the congruent shapes are as follows: - Table spoons of the same size
- Tables
- Fan wings of the same brand
- Chocolates of the same size
∠A ↔ ∠F, ∠B ↔ ∠E, ∠C ↔ ∠D; AB ↔FE, BC ↔ED, AC↔ FD
Let's consider these two triangles. Since these triangles are congruent, The angles of these two triangles are congruent. - ∠A ↔ ∠F
- ∠B ↔ ∠E
- ∠C ↔ ∠D
The sides of these two triangles are also congruent. - AB ↔FE
- BC ↔ED
- AC↔ FD
∠E of the triangle DEF corresponds to the ∠C of the triangle BCA.
EF of the triangle DEF corresponds to the CA of the triangle BCA.
∠F of the triangle DEF corresponds to the ∠A of the triangle BCA.
DF of the triangle DEF corresponds to the BA of the triangle BCA. ## Exercise 7.2
Here, PE is the equivalent side of the AR.
Here, EN is the equivalent side of the RT.
Here, PN is the equivalent side of the AT.
Here, EN is the equivalent side of the RT. and
Here, AT is the equivalent side of the PN.
The equivalent angles are ∠RAT = ∠EPN.
The other equivalent angles are ∠ATR = ∠PNE. Thus, the three equal parts according to the ASA criteria are: AT = PN (Given) ∠RAT = ∠EPN ∠RAT = ∠EPN
Hence, the given statement of the student is not justified.
AT = ON (Given) AR = OW (Given) ∠T = ∠N (Given) ∠R = ∠W (Given) ∠A = ∠O (Given) Hence, the two triangles are congruent.
In the given two triangles, the three pairs of equal parts are: BT = BC (Given) AT = AC (Given) ∠TAB = ∠CAB (right angle) Hence, the two triangles are congruent according to the SAS criteria.
In the given two triangles, the three pairs of equal parts are: RS = PQ (Given) QS = TQ (Given) ∠QSR = ∠PQT Hence, the two triangles are congruent according to the SAS criteria.
Let's draw the two congruent triangles on the square sheet. In the given two triangles, the three pairs of equal parts are: BC = EF (Side) AB = DE (Side) AC = DF (Side) Hence, the two triangles are congruent according to the SSS criteria.
Let's draw the two non-congruent triangles on the square sheet. Perimeter is equal to the sum of the three sides of the triangle. Since the two triangles are not congruent, their perimeter will be unequal. AB + BC + CA is not equal to DE + EF + DF
In the given two triangles, the five pairs of equal parts are: BC = EF (Side) AB = DE (Side) ∠C = ∠F ∠B = ∠E ∠A = ∠D But, it does not follow any criterion for the congruency. Hence, the given two triangles are not congruent.
In the given two triangles, the three pairs of equal parts are: BC = QR ∠C = ∠R (Given) ∠B = ∠Q (Right angle) Hence, the two triangles are congruent as per the ASA criteria.
BC = DE (Given) ∠A = ∠F (Given) ∠B = ∠E (Right angle) Hence, the two triangles are congruent as per the ASA criteria. |