Question

Which congruency rule(s) is/are used to prove the construction of a perpendicular bisector?

• A. SAS
• B. SSS
• C. RHS
• D. ASS

Answer 1

Answer: (A), (B)

The correct options are
A SAS
B SSS


In $△$ PAQ and $△$PBQ
AP = BP ; AQ = BQ (Equal radii)
PQ = PQ (Common side)
$\therefore$ $△$PAQ $\cong$ $△$PBQ [SSS rule]
So $\angle APQ=\angle BPQ$.... CPCT

Now In $△$ APO and $△$ BPO
AP = BP (Equal radii)
$\angle APO=\angle BPO$ (Proved above)
OP = OP (Common)
$\therefore$ $△$APO $\cong$ $△$BPO [SAS rule]

So OA = OB and
$\angle AOP=\angle BOP$ [CPCT]
But, $\angle AOP+\angle BOP$ = 180° [Linear pair]
$\Rightarrow$ $2\angle AOP$= 180°
$\Rightarrow$ $\angle AOP$= 90°

Thus we can see SSS and SAS congruency rules are used in the above proof.