Question

prove that a triangle is isosceles if and only if two altitudes are congruent.

prove both ways

Answer 1

A let A B C be iso seeles triangle with AB=AC Also let an Þ BP and CB be two altitudes . B tence we have to prove that BP @ A ABP and For the triangles AAeg, LAPB = LAQC = 90° i) ü) ü) AB= АС, is ZBAC common angle Hence ДАВР у ДС 9 (using "Ras' congruency law) BP ~ CB consequently (Proved) Only if: let ABC a triangle with BP and co be two altitude such that BP ICQ

prove that a ABC is isosceles We have to triangle iei, AB - AC Now, for for two two triangles A ABP and & ACS, i) BP cao ü ) LBAC is common common angle L BPA = LegA = 90° fence ДАВР УДАс g that Consequently, we can we can conclude AB=AC isosceles triangle ''. A ABC flence the proof

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