# NCERT Solutions for Class 7 Maths Chapter 7 Exercise 7.1

NCERT Solutions for Class 7 Maths Chapter 7 Exercise 7.1 (Ex. 7.1) Congruence of Triangles updated for academic session 2020-2021 CBSE and State board. All the solutions are in PDF and videos format free to use online or download without any login.

In class 7 math exercise 7.1, we learn how to check whether two triangles are congruent or not. Questions are simple to understand and easy to solve. Practice all the questions taking help from PDF and Videos solutions.## Class 7 Maths Chapter 7 Exercise 7.1 Solution

Class: 7 | Mathematics |

Chapter: 7 | Congruence of Triangles |

Exercise: 7.1 | Hindi and English Medium Solution |

### CBSE NCERT Class 7 Maths Chapter 7 Exercise 7.1 Solution in Hindi and English Medium

### Class 7 Maths Chapter 7 Exercise 7.1 Solution in Videos

#### Congruent Figures

If they cover each other exactly then clearly they are of the same shape and same size. This method of comparing two figures is known as the method of superposition. Clearly, a figure and its carbon copy are of the same shape and size.

#### Congruent Figures:

If two figures have exactly the same shape and size, they are said to be congruent. Two plane figures are congruent if each when superposed on the other, covers it exactly.

###### Some Types of Congruent Figures

##### Congruence of Triangles:

Two triangles are congruent if pairs of corresponding sides and corresponding angles are equal.

Thus, triangle ABC ≅ triangle DEF, if AB = DE, BC = EF and CA = FD, ∠A = ∠D, ∠B = ∠E and ∠C = ∠F.

It may be kept in mind that while superposing one triangle on another triangle which is congruent to it, we match the corresponding vertices.

##### Case 1: (SSS congruence condition):

Two triangles are congruent if the three sides of one triangle are respectively equal to the three sides of the other triangle.

##### Find triangle ABC and triangle PQR are congruent. If AB = 5 cm, BC = 6.5 cm and CA = 4 cm and PQ = 5 cm, QR = 6.5 cm and PR = 4 cm.

Draw a triangle ABC with AB = 5 cm, BC = 6.5 cm and CA = 4 cm.

Draw another triangle PQR with PQ = 5 cm, QR = 6.5 cm and PR = 4 cm.

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. Thus, AB = PQ; BC = QR and CA = RP.

We observe that the two triangles cover each other exactly.

So, triangle ABC ≅ triangle PQR.

##### Case 2: (SAS congruence condition):

Two triangles are congruent if the two sides and the included angle of one are respectively equal to the two sides and the included angle of the other.

##### Find triangle ABC and triangle PQR are congruent. If AB = 5 cm, BC = 6.5 cm and ∠B = 60° and PQ = 5 cm, QR = 6.5 cm and ∠Q = 60°. .

Draw a triangle ABC with AB = 5 cm, BC = 6.5 cm and ∠B = 60°.

Also, draw triangle PQR with PQ = 5 cm, QR = 6.5 cm and ∠Q = 60°.

Thus, we have: AB = PQ, BC = QR and ∠B = ∠Q.

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.

We observe that the two triangles will cover each other exactly.

So, triangle ABC ≅ triangle PQR.

##### Is congruent triangles are similar?

Two triangles are congruent if they have the same three sides and exactly the same three angles. (Note: If two triangles have three equal angles, they need not be congruent. All that we know is these triangles are similar.) SAS: “Side, Angle, Side”.

##### How are congruent triangles used in real life?

By utilizing congruent triangles, the buildings create a nice work atmosphere (office buildings), a protection system from the sun by reflecting off opposite triangular faces, or even a popular tourist attraction. This is an example of triangle congruence in the real world- identical buildings.

##### How do you prove triangles are congruent?

If two sides and the included angle of one triangle are equal to the corresponding sides and angle of another triangle, the triangles are congruent.