class 10th chapter - triangles. plz answer the question I will mark you as brainlist
Share
class 10th chapter - triangles. plz answer the question I will mark you as brainlist
Sign Up to our social questions and Answers Engine to ask questions, answer people’s questions, and connect with other people.
Login to our social questions & Answers Engine to ask questions answer people’s questions & connect with other people.
Step-by-step explanation:
(I).In ∆PQR and ∆PQS:
angle P=angle S.(90°).
PQ=PQ(common)
∆PQR~∆PQS:(AA criteria)
so, QS/PQ=PQ/QR
=> PQ×PQ=QS×QR
: PQ²=QS×QR.
(ii).In ∆PQR and ∆SPR:
angle P=angle S.(90°).
PR=PR(common)
∆PQR~∆SPR:(AA criteria)
so, SR/PR=PR/QR
=> PR×PR=QR×SR
: PR²=QR×SR.
(iii).In ∆PQS and ∆PRS:
Angle S=Angle S(common)
Now, Angle P in ∆PQR is 90°.
=>QPS+RPS=90°.------(1)
Also, Angle S in ∆PQS is 90°.
=> PQS+PSQ+QPR=180°.
=> PQS+QPS=180°-90°=90°.-----(2)
By (2)-(1):
=> PQS+QPS-(QPS+RPS)=90°-90°.
=> PQS+QPS-QPS-RPS=0°
=> PQS=RPS.
∆PQS~∆PRS:(AA criteria)
so, QS/PS=PS/SR.
=> QS×SR=PS×PS.
=> PS²=QS×SR.