Question

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Answer 1

Given: Triangle are isosceles

Proof :In TriangleACD and Triangle CDB

SegAC=SegCB...........triangle is isosceles.(1)

SegAD=SegDB...........D is midpoint of AB..(2)

SegCD=SegCD........... common side.....(3)

So from (1), (2), (3) by SSS-side side side test

Triangle ACD congruent to Triangle CDB.........4

Therefore AngleCDA=AngleCDB....(5)

AB is a line which equals to 180degree. D is the point in AB such that AD=DB(6)

From(4) (5) (6),

AngleACD and Angle CDB can only be equal if it's 90 degree.

Therefore seg CD is perpendicular bisector so CDperpendicularAB.