Congruence of Triangles Class 7 Notes: Chapter 7

Chapter 7 Congruence of triangles of class 7 Maths discusses the congruence of triangles in particular. Along with that, the congruence of plane figures, line segments and angles are also discussed.

What is Congruence?

Two objects that are exact copies of one another are known as congruent objects. This relation of two objects being congruent is known as congruence.

Congruence of Plane Figures

Congruence of Triangles Class 7 Notes

Two plane figures F1 and F2 are said to be congruent if the trace-copy of F1 fits exactly on that of F2. We denote it as F1 ≅ F2

Congruence Among Line Segments

Congruence of Triangles Class 7 Notes

Two line segments, AB and CD, are said to be congruent if they have equal lengths. We denote this as \(\overline{AB}≅\overline{CD}\)

Congruence of Angles

Congruence of Triangles Class 7 Notes

Two angles, ∠ABC and ∠PQR, are said to be congruent if their measures are equal. We Denote it as ∠ABC ≅ ∠PQR or as m∠ABC = m∠PQR.

Congruence of Triangle

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

Congruence of Triangles Class 7 Notes

In the given figure, both the triangles have the same shape and size. Hence they are said to be congruent and the congruence between them is expressed as ∆ABC ≅ ∆PQR

The four criteria for congruence of triangles are as follows:

  • SSS Congruence of two triangles – Two triangles, under a given correspondence, are congruent if the three sides of one of the triangles are equal to the three corresponding sides of the other
  • SAS Congruence of two triangles – Two triangles, under a given correspondence, are congruent if two sides and the angle included between them in one of the triangles are equal to the corresponding sides and the angle included between them of the other triangle.
  • ASA Congruence of two triangles – Under a given correspondence, two triangles are congruent if two angles and the side included between them in one of the triangles are equal to the corresponding angles and the side included between them of the other triangle.
  • RHS Congruence of two right-angled triangles – Under a given correspondence, two right-angled triangles are congruent if the hypotenuse and a leg of one of the triangles is equal to the hypotenuse and the corresponding leg of the other triangle.

It should be noted that two triangles with equal corresponding angles need not necessarily be congruent.

Congruence Of Triangles Class 7 Questions

  1. In the figure, the two triangles are congruent. The corresponding parts are marked. We can write ∆RAT ≅ ?
  2. Congruence of Triangles Class 7 Notes

  3. 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?
  4. Draw a rough sketch of two triangles such that they have five pairs of congruent parts but still, the triangles are not congruent.
  5. Explain, why ∆ABC ≅ ∆FED?
  6. Congruence of Triangles Class 7 Notes

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Practise This Question

The term perimeter is defined only for polygons. Say true or false.