SOLUTION: in triangle ABC, the altitudes to the side AB and AC are congruent. Prove that quadrilateral PBCQ is: a. trapezoid b. isosceles trapezoid

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Question 682141: in triangle ABC, the altitudes to the side AB and AC are congruent. Prove that quadrilateral PBCQ is:
a. trapezoid
b. isosceles trapezoid
Answer by vidya p(12) (Show Source):
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Solution :
In triangle ABC, Altitude from B and C are equal with each other. hence we have:
BQ = PC
now consider two triangle PBC and Triangle QCB
we have BC = CB is the common sides.
BQ = PC given equal altitudes.
Hence by RHS rule ,
Triangle PBC is congruent to Triangle QCB.
PB = QC by ( CPCT )
also these two triangles are congruent then there height must be equal , hence we
can say that they must lie between the parallel lines ( PQ and BC )
hence PBQC is the ISOSCELES Trapezoid ( since PQ parallel BC and PB = QC )