Question

PT is an altitude of an isosceles triangle PQR in which PQ=PR.Show that i) PT bisects OR ii) PT bisects angle p

Answer 1

given:PQ=PR

to prove:(1) QT=TR

(2) angle QPT = angle RPT

proof:in ∆PQT & ∆PTR

PT=PT (common)

PQ=PR (given)

angle PTQ=angle PTR (pt perpendicular to qr)

hence, ∆PQT congurence to ∆PTR. (by sas rule)

QT=RT. ( by cpct )

angle TPQ = angle TPR (by cpct)

proved.....