# NCERT Solutions for Class 7 Maths Chapter 7 Exercise 7.2

NCERT Solutions for Class 7 Maths Chapter 7 Exercise 7.2 (Ex. 7.2) Congruence of Triangles in Hindi and English Medium free to use online or download in PDF. All the question answers and solutions as well, are done by the subject experts using simple steps.

In class 7 math exercise 7.2, we will learn the criteria of congruence like SAS, SSS, ASA, and RHS. Exercise 7.2 is important not only for class 7, but the next classes also.## Class 7 Maths Chapter 7 Exercise 7.2 Solution

Class: 7 | Mathematics |

Chapter: 7 | Congruence of Triangles |

Exercise: 7.2 | PDF and Videos Solution |

### CBSE NCERT Class 7 Maths Chapter 7 Exercise 7.2 Solution in Hindi and English Medium

### Class 7 Maths Chapter 7 Exercise 7.2 Solution in Videos

##### Case 3: (ASA congruence condition):

Two triangles are congruent if the two angles and the included side of one are respectively equal to the two angles and the included side of the other triangle.

##### Show that triangle ABC and triangle PQR are conguent if BC = 6 cm, ∠B = 55° and ∠C = 40° and QR = 6 cm, ∠Q = 55° and ∠R = 40°.

Draw a triangle ABC with BC = 6 cm, ∠B = 55° and ∠C = 40°.

Draw another triangle PQR with QR = 6 cm, ∠Q = 55° and ∠R = 40°.

Thus, we have: BC = QR, ∠B = Q and ∠C = R.

Make a copy of DABC on a tracing paper and try to make it cover DPQR with A on P, B on Q and C on R. We observe that the two triangles cover each other exactly.

So, triangle ABC ≅ triangle PQR.

##### Case 4: (RHS congruence condition):

Two right triangles are congruent if the hypotenuse and one side of the first triangle are respectively equal to the hypotenuse and one side of the second.

##### Show that triangle ABC and triangle PQR are conguent if ∠B = 90°, AB = 6 cm and hypotenuse AC = 10 cm and ∠Q = 90°, PQ = 6 cm and hypotenuse PR = 10 cm.

Draw a triangle ABC with ∠B = 90°, AB = 6 cm and hypotenuse AC = 10 cm. Also, draw a triangle PQR with ∠Q = 90°, PQ = 6 cm and hypotenuse PR = 10 cm. Thus, in triangle ABC and triangle PQR, we have:

∠B = ∠Q = 90°, AB = PQ, hypotenuse AC = hypotenuse PR. Make a copy of triangle ABC on a tracing paper and try to make it cover triangle PQR with A on P, B on Q and C on R. You would observe that the two triangles cover each other exactly.

So, triangle ABC ≅ triangle PQR.

##### Congruence and Area:

It is clear that two congruent figures are equal in area. But, there can be two figures which are equal in area and yet, they may not be congruent. For example, if we consider two rectangles with dimensions 4 cm by 3 cm and 6 cm by 2 cm respectively then they are equal in area. But, clearly, they are not congruent.

##### Without drawing the triangles, state the correspondence between the sides and the angles of the following pairs of congruent triangles: (i) triangle ABC ≅ triangle QRP (ii) triangle ABC ≅ triangle PRQ

(i) When triangle ABC = triangle QRP, we have: A ↔ Q, B ↔ R, C ↔ P.

So, AB = QR, BC = RP, AC = QP.

∠A = ∠Q, ∠B = ∠R and ∠C = ∠P.

(ii) When triangle ABC = triangle PRQ,

we have: A ↔ P, B ↔ R and C ↔ Q.

So, AB = PR, BC = RQ, AC = PQ,

∠A = ∠P, ∠B = ∠R and ∠C = ∠Q.

##### If two triangles have their corresponding angles equal, are they always congruent?

If the all three corresponding angles are equals of two triangles then, two triangles may be congruent or not but they are similar.

##### Why is congruence important in real life?

Congruent Triangles are an important part of our everyday world, especially for reinforcing many structures. Two triangles are congruent if they are completely identical. This means that the matching sides must be the same length and the matching angles must be the same size.

##### what is difference between similarity and congruence?

When two line segments have the same length, they are congruent. When two figures have the same shape and size, they are congruent. Similar means that the figures have the same shape, but not the same size.

##### Why congruence is a special case of similarity?

Clearly, congruence is a special case of similarity, i.e., all congruent triangles are similar, but only some similar triangles are congruent.

##### Is AAA a congruence theorem?

As you can see in the video, triangles that have 3 pairs of congruent angles do not necessarily have the same size. AAA (Angle-Angle-Angle) is not a congruence rule!