Question 246288
Triangle is ABC.


AD intersects AC at D.


It's a median so it splits the line AC into 2 equal parts.


You have:


AB = BC (legs of isosoceles triangle)

AD = DC (median splits AC into 2 equal parts by definition)


BD = BD (identity - same line segment is equal to itself)


triangles ABD and DBC are congruent (sss)


angle ADB = angle CDB (corresponding angles of congruent triangles are equal).


angle ADB and CDB are supplementary (their sum is equal to 180 degrees because their outer line segments form a straight line).


angle ADB and angle CDB must each be 90 degrees (they are equal and their sum is equal to 180.).


angle ADB and angle CDB are right angles (right angle = 90 degrees).


BD is perpendicular to AC (intersects at a right angle therefore is perpendicular).


or something like that.


you prove the angles are congruent.


you prove the angles have to be right angles.


that proves that the median is also an altitude because an altitude is perpendicular to the base by definition.