Q153 of 158 Page 159

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?

Formula Used/Theory:-


→ when 2 angles and side between both the angles are equal in both the triangles then triangles are congruent by ASA congruence criterion


In ∆ABC and ∆DCB


∠B = ∠C (Both 70° )


∠ACB = ∠DCB (Both 30° )


BC = BC (common)


∆ABC ≅ ∆DCB


⇒ Hence; both triangles are congruent by ASA congruence


If ∆ABC ≅ ∆DCB then;


If triangles are congruent then all 3 sides of triangle are equal to all 3 sides of other triangle


BC = BC


⇒ AB = DC


⇒ AC = DB


More from this chapter

All 158 →
151

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

 152

In Fig. 6.53, ∠1 = ∠2 and ∠3 = ∠4.

(i) Is ∆ADC ≅ ∆ABC? Why?


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


 154

In Fig. 6.55, QS ⊥ PR, RT ⊥ PQ and QS = RT.


(i) Is ∆QSR ≅ ∆RTQ? Give reasons.


(ii) Is ∠PQR = ∠PRQ? Give reasons.

 155

Points A and B are on the opposite edges of a pond as shown in Fig. 6.56. To find the distance between the two points, the surveyor makes a right-angled triangle as shown. Find the distance AB.