Proof for Validity of Construction of a Perpendicular Bisector
Which congrue...
Question
Which congruency rule(s) is/are used to prove the construction of a perpendicular bisector?
A
SAS
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B
SSS
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C
RHS
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D
ASS
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Solution
The correct options are A SAS B SSS In △ PAQ and △PBQ AP = BP ; AQ = BQ (Equal radii) PQ = PQ (Common side) ∴△PAQ ≅△PBQ [SSS rule] So ∠APQ=∠BPQ.... CPCT
Now In △ APO and △ BPO AP = BP (Equal radii) ∠APO=∠BPO (Proved above) OP = OP (Common) ∴△APO ≅△BPO [SAS rule]
So OA = OB and ∠AOP=∠BOP [CPCT] But, ∠AOP+∠BOP = 180° [Linear pair] ⇒2∠AOP= 180° ⇒∠AOP= 90°
Thus we can see SSS and SAS congruency rules are used in the above proof.