Q 38 In the adjoining figure, TR = TS, ∠1=2∠2 and ∠4=2∠3 Prove that RB = SA - Maths - Congruency of Triangles

Question

Q 38 In the adjoining figure, TR = TS, ∠ 1 = 2 ∠ 2
  a n d   ∠ 4 = 2 ∠ 3 Prove that RB = SA

Shruti Tyagi · Accepted Answer

Dear student,
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In ∆RTS, we haveST=RT⇒∠TRS=∠TSR     
(i)      
(equal sides have equal angles opposites to them)We have,∠1=∠4      
(vertically opp
angles)⇒2∠2=2∠3    
[∵∠1=2∠2 and ∠4=2∠3   given]⇒∠2=∠3      
(ii)Subtracting (ii) from (i) we get,∠TRS-∠2 =∠TSR-∠3 ⇒∠TRB=∠TSA        
(iii)Thus in ∆RBT and ∆SAT, we have∠RTB=∠STA        
(common)RT=ST      
(given)and, ∠TRB=∠TSA       from (iii)So, by ASA congruence criterion, we have∆RBT≅△SAT⇒RB=SA     
(CPCT)
Regards

Q.38. In the adjoining figure, TR = TS, ∠ 1 = 2 ∠ 2 a n d ∠ 4 = 2 ∠ 3 . Prove that RB = SA.

Q.38. In the adjoining figure, TR = TS, $∠ 1 = 2 ∠ 2 a n d ∠ 4 = 2 ∠ 3$ . Prove that RB = SA.