Question

In the given figure, it is given that RT = TS, 1 =  2 and 4 = 3.

Prove that:

(i) RBT   SAT (ii) RB = AS​

Answer 1

Answer:

Step-by-step explanation:

In ΔRTS, we have  

RT=ST

⇒∠TSR=∠TRS (i)

We have,

∠1=∠4  [Vertically opposite 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 triangles, RBT and SAT, we have  

∠RTB=∠STA [Common]

RT=ST  [Given]

and, ∠TRB=∠TSA [From (iii)]

So, by ASA congruence criterion, we obtain

ΔRBT≅ΔSAT

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