# NCERT Class 7 Maths Congruence of Triangles

NCERT Class 7 Maths Congruence of Triangles. Download NCERT Chapters and Books in pdf format. Easy to print and read. Copies of these textbooks may be downloaded and used as textbooks or for reference. Refer to other chapters and books at other links (NCERT now providing you soft copies of all textbooks of all subjects from class first to twelfth online).

Congruence of Triangles

7.1 INTRODUCTION

You are now ready to learn a very important geometrical idea, Congruence. In particular, you will study a lot about congruence of triangles. To understand what congruence is, we turn to some activities. The relation of two objects being congruent is called congruence. For the present, we will deal with plane figures only, although congruence is a general idea applicable to three-dimensional shapes also. We will try to learn a precise meaning of the congruence of plane figures already known.

7.2 CONGRUENCE OF PLANE FIGURES

Look at the two figures given here (Fig 7.3). Are they congruent? You can use the method of superposition. Take a trace-copy of one of them and place it over the other. If the figures cover each other completely, they are congruent. Alternatively, you may cut out one of them and place it over the other. Beware! You are not allowed to bend, twist or stretch the figure that is cut out (or traced out). In Fig 7.3, if figure F1 is congruent to figure F2 , we write F1 ≅ F2.

7.3 CONGRUENCE AMONG LINE SEGMENTS

When are two line segments congruent? Observe the two pairs of line segments given here (Fig 7.4). Use the ‘trace-copy’ superposition method for the pair of line segments in [Fig 7.4(i)]. Copy CDand place it on AB. You find that CD covers AB, with C on A and D on B. Hence, the line segments are congruent. We write AB ≅ CD. Repeat this activity for the pair of line segments in [Fig 7.4(ii)]. What do you find? They are not congruent. How do you know it? It is because the line segments do not coincide when placed one over other.

You should have by now noticed that the pair of line segments in [Fig 7.4(i)] matched with each other because they had same length; and this was not the case in [Fig 7.4(ii)]. In view of the above fact, when two line segments are congruent, we sometimes just say that the line segments are equal; and we also write AB = CD. (What we actually mean is AB≅ CD)

7.4 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. We extend this idea to triangles.

Two triangles are congruent if they are copies of each other and when superposed, they cover each other exactly.

ΔABC and ΔPQR have the same size and shape. They are congruent. So, we would express this as

ΔABC ≅ ΔPQR

This means that, when you place ΔPQR on ΔABC, P falls on A, Q falls on B and R falls on C, also falls along AB , QR falls along BCand PR falls along AC. If, under a given correspondence, two triangles are congruent, then their corresponding parts (i.e., angles and sides) that match one another are equal. Thus, in these two congruent triangles, we have:

Corresponding vertices : A and P, B and Q, C and R.

Corresponding sides : ABand PQ, BC and QR , AC and PR .

Corresponding angles : ∠A and ∠P, ∠B and ∠Q, ∠C and ∠R.

If you place ΔPQR on ΔABC such that P falls on B, then, should the other vertices also correspond suitably? It need not happen! Take trace, copies of the triangles and try to find out.

This shows that while talking about congruence of triangles, not only the measures of angles and lengths of sides matter, but also the matching of vertices. In the above case, the correspondence is

A ↔P, B ↔ Q, C ↔ R

We may write this as ABC ↔PQR

Please refer to attached file for NCERT Class 7 Maths Congruence of Triangles

## Tags:

Click to View or Download pdf file
Click for more Congruence of Lines and Angles Study Material

## Latest NCERT & CBSE News

Read the latest news and announcements from NCERT and CBSE below. Important updates relating to your studies which will help you to keep yourself updated with latest happenings in school level education. Keep yourself updated with all latest news and also read articles from teachers which will help you to improve your studies, increase motivation level and promote faster learning

### Board Exams FAQs released by CBSE

CBSE has released very important FAQs for class 10 and class 12 students who have given the board exams. Students have been coming up with lot of queries and have lot of questions relating to what are the next steps of CBSE. The following FAQs by CBSE will help to...

### Applied Mathematics Introduced by CBSE as Elective for Class 11 and Class 12

Mathematics Syllabus Revised by CBSE at the Senior Secondary Level! The Central Board of Secondary Education (CBSE) to offer 'Applied Mathematics' as an Elective for XI and XII standard students. The elective subject, Applied Mathematics, is focused at evolving an...

### Critical notice issued by CBSE relating to Boards and other classes

Critical notice issued by CBSE relating to Boards and other classes

### CBSE Boards Answer Sheet Evaluation Class 10 and Class 12

HRD Minister Ramesh Pokhriyal, through a video conference with all the education ministers of the state, discussed the further steps to be taken to smoothen the education process during the Covid-19 lockdown. The most important topic which was discussed repeatedly on...

### Procedure for correction in Name and Date of Birth

Procedure for correction in Name and Date of Birth in CBSE records Name Change: Applications regarding changes in name or surname of candidates will be considered provided the changes have been admitted by the Court of law and notified in the Government Gazette before...

### CBSE Recommends Arogya Setu App, Writes To School Principals

Written recommendation from CBSE to school principals for initiating the Arogya Setu App! New Delhi:  The Central Board of Secondary Education has advised all school principals through a written communication recommending the “Arogya Setu App” and Health Ministry's...

×