Question

Plz solve this all for 50 pts​

Answer 1

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 2

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