R is the mid point of PQ and Q is the mid point of RS verify that: PR=QS,RQ= QS, PR=RQ
Answers
Question:-
☞ R ɪs ᴛʜᴇ ᴍɪᴅ ᴘᴏɪɴᴛ ᴏғ PQ ᴀɴᴅ Q ɪs ᴛʜᴇ ᴍɪᴅ ᴘᴏɪɴᴛ ᴏғ RS ᴠᴇʀɪғʏ ᴛʜᴀᴛ: PR=QS,RQ= QS, PR=RQ.
To Find:-
☞ Vᴇʀɪғʏ ᴛʜᴀᴛ: PR=QS,RQ= QS, PR=RQ
Given:-
☞ R ɪs ᴛʜᴇ ᴍɪᴅ ᴘᴏɪɴᴛ ᴏғ PR
Solution:-
PR = QS (1)
Aɢᴀɪɴ, R ɪs ᴛʜᴇ ᴍɪᴅ ᴘᴏɪɴᴛ ᴏғ QS
QR = PQ (2)
Nᴏᴡ, PR=QS,RQ= QS, PR=RQ
☞ PR = 3 QS [ Usɪɴɢ (1) ᴀɴᴅ (2) ]
☞ QS = 1/3 PS
Oɴ ᴘᴜᴛᴛɪɴɢ ᴠᴀʟᴜᴇ ᴏғ QS ɪɴ (1), Wᴇ ɢᴇᴛ :-
☞ PR = 1/3 PS
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Given : R is the mid-point to PQ
Q is the mid-point of RS.
To Find : Verify that PR = QS
Solution:
Let say PQ = 2X
R is the mid-point to PQ
=> PR = QR = PQ/2
=> PR = QR = 2X/2
=> PR = QR = X
Q is the mid-point of RS.
=> QR = QS = RS/2
QR = X
=> QS = RS/2 = X
=> QS = X
PR = QR = QS = X
=> PR = QS
QED
Hence proved
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