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Congruent triangles
1.
AB and CD bisect each other. Prove that :
(1) ∆OAD is congruent to ∆OBC
(2) AD || BC
2.
AD is the bisector of ∠BAC. AB = AC. Prove that
(1) ∆ABD is congruent to ∆ACD
(2) BD = CD
3.
In isosceles ∆ABC with AB = AC, D and E are chosen
on sides AB and AC such that AD = AE. Prove that
(1) ∆ABE is congruent to ∆ACD
(2) BE = CD
4.
B is the midpoint of line segment AC. AD || BE and BD || CE. Prove that
∆ABD is congruent to ∆BCE
