Ninth icse
asked Jul 2, 2016 in Geometry Answers by Savitha

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The picture shows an isosceles triangle fitting the description.

BO=OC (because O is the midpoint of BC).

BRO=OSC=90º by definition.

Angle ABC=ACB (given, equal angles of triangle ABC).

Angle ROB=SOC=90-ABC=90-ACB (angles in a right-angled triangle).

Triangles ROB and SOC are congruent because all the angles and the hypotenuses are equal.

Therefore OR=OS and BR=SC.

Angle PCB=90-ABC and angle QBC=90-ACB so PCB=QBC.

BC is common to triangles BPC and BQC. Angle BPC=BQC=90º by definition.

Triangles BPC and BQC are congruent (all angles and hypotenuses are equal).

Therefore PC=BQ.

answered Jul 2, 2016 by Rod Top Rated User (486,900 points)
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