geometrical verification of mid point theorem
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Given :- AP=PB, AQ=QC.
To prove:
PQ || BC and PQ=1/2 BC
To prove ∆ APQ congrent ∆ QRC
Proof steps:
AQ=QC [midpoint]
∠ APQ = ∠QRC [Corresponding angles]
∠PBR=∠QRC=∠APQ [Corresponding angles].
∠RQC=∠PAQ [When 2 pairs of corresponding angles are congruent in a triangle, the third pair is also congruent.]
Therefore , ▲APQ ≅ ▲QRC
Hence prooved
AP=QR=PB and PQ=BR=RC.
To prove:
PQ || BC and PQ=1/2 BC
To prove ∆ APQ congrent ∆ QRC
Proof steps:
AQ=QC [midpoint]
∠ APQ = ∠QRC [Corresponding angles]
∠PBR=∠QRC=∠APQ [Corresponding angles].
∠RQC=∠PAQ [When 2 pairs of corresponding angles are congruent in a triangle, the third pair is also congruent.]
Therefore , ▲APQ ≅ ▲QRC
Hence prooved
AP=QR=PB and PQ=BR=RC.
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