Page 48 - Mathematics Class - IX
P. 48
3. In the pair of ∆PQR and ∆STU,
QR = TU = ..................., PQ = ..................., ST = ...................,
PR = ..................., SU = .................... ∠S = ...................,
∠Q = ∠T = ..................., ∠R = ∠U = ..................., ∠P = ....................
Hence, ∆PQR ≅ ∆STU
4. In the pair of ∆YXZ and ∆MLN,
hypotenuse YZ = hypotenuse MN = ................
XZ = LN = ..................., XY = ...................,
LM = ..................., ∠X = ∠L = ....................,
∠Y = ..................., ∠M = ....................,
∠Z = ..................., ∠N = ....................,
Hence, ∆YXZ ≅ ∆MLN
INFERENCE
Using triangle cut outs, we have verified experimentally the different criteria for congruency of triangles.
EXTENDED TASK
1. Derive the minimum number of conditions of congruency for a given polygon of n sides. For example,
triangles require congruency of at least three corresponding elements whereas circles require only one
condition.
APPLICATION
These criteria are useful in
1. Solving many problems in geometry.
2. Practical problems such as finding width of a river without crossing it.
46
