![]() ![]() Give the correspondence between the triangle in Fig. 7.4 (iii),Ĥ 112 MATHEMATICS FD AB, DE BC and EF CA and F A, D B and E C So, Δ FDE Δ ABC but writing Δ DEF Δ ABC is not correct. That is, P corresponds to A, Q to B, R to C and so on which is written as P A, Q B, R C Note that under this correspondence, Δ PQR Δ ABC but it will not be correct to write ΔQRP Δ ABC. Also, there is a one-one correspondence between the vertices. That is, PQ covers AB, QR covers BC and RP covers CA P covers A, Q covers B and R covers C. Notice that when Δ PQR Δ ABC, then sides of Δ PQR fall on corresponding equal sides of Δ ABC and so is the case for the angles. ![]() If Δ PQR is congruent to Δ ABC, we write Δ PQR Δ ABC. 7.4 (ii), (iii) and (iv) are congruent to Δ ABC while Δ TSU of Fig 7.4 (v) is not congruent to Δ ABC. 7.4 (ii) to (v) and turn them around and try to cover Δ ABC. 7.4 Cut out each of these triangles from Fig. You already know that two triangles are congruent if the sides and angles of one triangle are equal to the corresponding sides and angles of the other triangle.ģ TRIANGLES 111 Now, which of the triangles given below are congruent to triangle ABC in Fig. Let us now discuss the congruence of two triangles. 7.3 (ii) and (iii) are obviously not congruent to the one in Fig 7.3 (i), but the square in Fig 7.3 (iv) is congruent to the one given in Fig 7.3 (i). Can you think of some more examples of congruent figures? Now, which of the following figures are not congruent to the square in Fig 7.3 (i) : Fig. So, you can find numerous examples where congruence of objects is applied in daily life situations. Obviously, if the two refills are identical or congruent, the new refill fits. Sometimes, you may find it difficult to replace the refill in your pen by a new one and this is so when the new refill is not of the same size as the one you want to remove. ![]() So, whenever identical objects have to be produced, the concept of congruence is used in making the cast. The cast used for moulding in the tray also has congruent depressions (may be all are rectangular or all circular or all triangular). Observe that the moulds for making ice are all congruent. You all must have seen the ice tray in your refrigerator. ![]() 7.2 You may wonder why we are studying congruence. You will observe that the squares are congruent to each other and so are the equilateral triangles. 7.2) or by placing two equilateral triangles of equal sides on each other. What do you observe? They cover each other completely and we call them as congruent circles.Ģ 110 MATHEMATICS Repeat this activity by placing one square on the other with sides of the same measure (see Fig. Now, draw two circles of the same radius and place one on the other. Do you remember what such figures are called? Indeed they are called congruent figures ( congruent means equal in all respects or figures whose shapes and sizes are both the same). You may recall that on placing a one rupee coin on another minted in the same year, they cover each other completely. Similarly, two bangles of the same size, two ATM cards issued by the same bank are identical. 7.1 You must have observed that two copies of your photographs of the same size are identical. You have already verified most of these properties in earlier classes. In this chapter, you will study in details about the congruence of triangles, rules of congruence, some more properties of triangles and inequalities in a triangle. In Chapter 6, you have also studied some properties of triangles. 7.1) AB, BC, CA are the three sides, A, B, C are the three angles and A, B, C are three vertices. For example, in triangle ABC, denoted as Δ ABC (see Fig. A triangle has three sides, three angles and three vertices. You know that a closed figure formed by three intersecting lines is called a triangle. 1 CHAPTER 7 TRIANGLES 7.1 Introduction You have studied about triangles and their various properties in your earlier classes. ![]()
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