Question

PQRS is a parallelogram if diagonals are equal. Find the value of angle SPQ.

plz tell fast

Answer 1

Answer:

Therefore, the incorrect statement is AQ=PQ.

We have ∠SPQ=60 degree

∠P+∠Q=180 (adj. ∠s of a || gm are supp)

∠Q=180 degree - 60 degree = 120 degree

Now PQ∣∣SR and AP is the transversal.

∴SAP=∠APQ=30∘ (∵AP bisects ∠SPQ)

∠SPA=∠SAP⇒SA=SP (isos. Δ property) ...(i)

Also ∠RAQ=∠AQP=60 degree

(PQ∣∣SR,AQ is transversal, alt ∠s)

and ∠AQP= 1/2 ∠PQR=60 degree

⇒∠RQA=∠RAQ (AQ bisect ∠PQR)

⇒RA=RQ (isos. Δ property) ....(ii)

∴ from eqn. (i) and (ii)

AS=AR (∵SP=RQ, opp. side of a ||gm)

Also, in ΔARQ,∠ARQ=60 degree

⇒ΔARQ is equilateral

⇒AR=RQ⇒AR=SP

Therefore, the incorrect statement is AQ=PQ.

Hope this answer helps you....

If you like my answer so please mark me as brainlist.....

And also...

Please do follow me....