Plz solve this all for 50 pts
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Answer:
Step-by-step explanation:
1) PS=PR ......(i)
So, ∠PSR=∠PRS (Base angles of isosceles triangle)
⇒ 180-∠PSR=180-∠PRS
⇒∠PST=∠PRQ ..... (ii)
∠TPS=∠QPR (given) .....(iii)
From (i), (ii) and (iii),
using ASA rule, we can state that
ΔPTS≅ΔPQR
By CPCT, we have PT=PR
∴proved.
2) In square PQRS, PQ=QR=RS=SP
In equilateral triangle RST, RS=ST=TR
Thus PS=QR (i) and ST=RT (ii)
Also, ∠PSR=∠QRS and ∠RST=∠TRS
So, ∠PSR+∠RST=∠QRS+∠TRS
⇒∠PST=∠QRT (iii)
From (i), (ii) and (iii),
using SAS rule,
ΔPST≅ΔQRT
By CPCT, PT=QT
∴proved.
3) [Sorry, I cannot draw, please excuse my not answering this question. You may not give me the Brainliest title if you wish.]
4) [This one too.]
Answer:
Step-by-step explanation:
1) PS=PR ......(i)
So, ∠PSR=∠PRS (Base angles of isosceles triangle)
180-∠PSR=180-∠PRS
∠PST=∠PRQ ..... (ii)
∠TPS=∠QPR (given) .....(iii)
From (i), (ii) and (iii),
using ASA rule, we can state that
ΔPTS≅ΔPQR
By CPCT, we have PT=PR
2) In square PQRS, PQ=QR=RS=SP
In equilateral triangle RST, RS=ST=TR
PS=QR (i) and ST=RT (ii)
∠PSR=∠QRS and ∠RST=∠TRS
So, ∠PSR+∠RST=∠QRS+∠TRS
∠PST=∠QRT (iii)
From (i), (ii) and (iii),
using SAS rule,
ΔPST≅ΔQRT