Question

in the given figure given below ,2AD=AB , P is the mid point of AB,Q is the mid point of DR and PR║ BS :
PROVE THAT :1) AQ ║ BS
2)DS = 3 RS

Answer 1

Given :-

• 2AD = AB
• P is the mid point of AB .
• Q is the mid point of DR .
• PR║ BS .

Solution :-

Given that , 2AD = AB and p is the midpoint of AB.

So,

→ AD = AP = PB

Now, in ∆DPR,

→ A and Q are the mid-point of DP and DR.

Therefore,

→ AQ || PR. { Mid Point Theorem .}

Hence ,

→ AQ || BS { Given, PR || BS . } (Proved.)

Now, in ∆ABC,

→ P is the midpoint of AB . {Given.}

and ,

→ PR || BS

Therefore,

→ R is the mid - point of BC .

Now, in ΔBRS and ΔQRC ,

→ ∠BRS = ∠QRC

→ BR = RC

→ ∠RBS = ∠RCQ

So,

→ ΔBRS ≅ ΔQRC .{ By ASA .}

Hence,

→ QR = RS . { By CPCT. }

So,

→ DS = DQ + QR + RS

→ DS = RS + RS + RS

→ DS = 3RS . (Proved.)

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