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From (2), can I automatically infer that AC is a bisector?

From the given figure,

when AC is perpendicular to BD, we won't be able to figure out anything about the triangles or the associated angles and we can't calculate what could possibly be the length of BD.

When BC = CD, C is mid-point of BD and AC is the median, still we can't comment on the length of BD in any possible way.

When both the given statements are considered together, we immediately realize that AC is both the angular bisector of A and altitude of the given triangle BAD. So we split BAD into two equally sized triangles BAC and ACD, such that AD = AB = 5. So, BD is obviously the full-hypotenuse of BAD and length is thus sqrt(2)*5. _________________

From (2), can I automatically infer that AC is a bisector?

From the given figure,

when AC is perpendicular to BD, we won't be able to figure out anything about the triangles or the associated angles and we can't calculate what could possibly be the length of BD.

When BC = CD, C is mid-point of BD and AC is the median, still we can't comment on the length of BD in any possible way.

When both the given statements are considered together, we immediately realize that AC is both the angular bisector of A and altitude of the given triangle BAD. So we split BAD into two equally sized triangles BAC and ACD, such that AD = AB = 5. So, BD is obviously the full-hypotenuse of BAD and length is thus sqrt(2)*5.

Thank you for the clear explanation. It helped a great deal. _________________

MBA Acceptance Rate by Country Most top American business schools brag about how internationally diverse they are. Although American business schools try to make sure they have students from...

McCombs Acceptance Rate Analysis McCombs School of Business is a top MBA program and part of University of Texas Austin. The full-time program is small; the class of 2017...