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प्रश्न
A line segment AB is bisected at point P and through point P another line segment PQ, which is perpendicular to AB, is drawn. Show that: QA = QB.
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उत्तर
Given: A ΔABQ in which AB is bisected at P
PQ is perpendicular to AB
We need to prove that
QA = QB
Proof:
In ΔAPQ and ΔBPQ
AP = PB ...[ P is the mid-point of AB ]
∠QPA = ∠QPB = 90° ...[ PQ is perpendicular to AB ]
PQ = PQ ...[ Common]
∴ By Side-Angel-Side criterion of congruence,
ΔQAP ≅ ΔQBP
The corresponding parts of the congruent triangles are
congruent.
∴ QA = QB ...[ c.p.c.t ]
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| Steps | Reasons | ||
| 1 | PM = QM | 1 | ... |
| 2 | ∠PMA = ∠QMA | 2 | ... |
| 3 | AM = AM | 3 | ... |
| 4 | ΔAMP ≅ ΔAMQ | 4 | ... |
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