Triangle ABS and triangle BDC is …

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Triangle ABS and triangle BDC is isosceles triangle on the same base BC and vertices A and D are on the same side of BC. If AD is extended to intersect BC at E. Show that
(1) triangle ABD congrent triangle ACD
(2) triangle ABE congrent triangle ACE
(3)AE is bisects angle A as well as angle D
(4)AE is the perpendicular bisector of BC
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