Mathematics
In the given figure, PA ⊥ AB; QB ⊥ AB and PA = QB. If PQ intersects AB at M, show that M is the mid-point of both AB and PQ.
Triangles
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Answer
Given,
⇒ PA = QB
From figure,
⇒ ∠PAM = ∠QBM = 90°
In △MAP and △MBQ,
⇒ ∠PAM = ∠QBM [Both equal to 90°]
⇒ AP = BQ [Given]
⇒ ∠AMP = ∠QMB [Vertically opposite angles are equal]
∴ △MAP ≅ △MBQ (By A.A.S axiom)
⇒ AM = MB [Corresponding parts of congruent triangles are equal]
⇒ PM = MQ [Corresponding parts of congruent triangles are equal]
Thus, M is the mid-point of both AB and PQ.
Hence, proved that M is the mid-point of both AB and PQ.
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