Page 187 - Start Up Mathematics_7

Example 7: In the following figures, lengths of the sides of the triangles are indicated. By applying

the SSS congruence rule, state which pairs of triangles are congruent? In case of
congruent triangles, write the result in symbolic form:

D L

5 cm
5 cm
(a) 3 cm 3 cm

E 6 cm F M 6 cm N

P

A
(b) 4 cm 5 cm
5 cm
2 cm

B 4 cm C Q 2.5 cm R

A

3.7 cm
(c) 3.7 cm

D
2.6 cm 2.6 cm
B C

Solution: (a) DE = LN, EF = NM, FD = ML

∴ ∆ DEF  ∆ LNM (by SSS congruence criterion)

(b) AC = PR (each 5 cm)

CB = PQ (each 4 cm)

BA ≠ QR

∴ ∆ ACB ≅ ∆ RPQ

(c) AB = AC (each 3.7 cm)

BD = CD (each 2.6 cm)

AD = AD (common)

∴ ∆ ABD  ∆ ACD (by SSS congruence criterion)

179