Q151 of 158 Page 159

In Fig. 6.52, DE = IH, EG = FI and ∠E = ∠I. Is ∆DEF ≅ ∆HIG? If yes, by which congruence criterion?

Given: DE = IH, EG = FI and ∠E = ∠I

Formula Used/Theory:-

→ when 2 sides and angle between both the sides are equal in both the triangles then triangles are congruent by SAS congruence criterion

In Δ DEF and Δ GIH

⇒ DE = HI (Given)

EG = FI

If we add length of GF both sides

EG + GF = FI + GF

⇒ EF = IG

⇒ ∠E = ∠I

∴ ∆DEF ≅ ∆HIG

Hence; Both triangles are congruent by SAS criterion

149

State which of the following pairs of triangles are congruent. If yes, write them in symbolic form (you may draw a rough figure).

A. ∆PQR : PQ = 3.5 cm, QR = 4.0 cm, ∠Q = 60°

∆STU : ST = 3.5 cm, TU = 4 cm, ∠T = 60°

B. ∆ABC : AB = 4.8 cm, A = 90°, AC = 6.8 cm

∆XYZ : YZ = 6.8 cm, ∠X = 90°, ZX = 4.8 cm

150

In Fig. 6.51, PQ = PS and ∠1 = ∠2.

(i) Is ∆PQR ≅ ∆PSR? Give reasons.

(ii) Is QR = SR? Give reasons.

152

In Fig. 6.53, ∠1 = ∠2 and ∠3 = ∠4.

(i) Is ∆ADC ≅ ∆ABC? Why?

(ii) Show that AD = AB and CD = CB.

153

Observe Fig. 6.54 and state the three pairs of equal parts in triangles ABC and DBC.

(i) Is ∆ABC ≅ ∆DCB? Why?

(ii) Is AB = DC? Why?

(iii) Is AC = DB? Why?