# Prove that segment BC is congruent to segment AD?

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• 1 month ago

The given conditions are not clear. I understand your problem as that

AB // CD

are given, & prove that BC=AD. If so, then

Proof:

BD=BD (common sides equal)

Thus, Tri. BCD is congruent to tri. DAB (A.S.A)

=>

BC=AD (the corresponding sides of 2 congruent triangles equal)

• sepia
Lv 7
1 month ago

Obviously, BC = AD, AB = DC,

• 1 month ago

In the figure itself it is seen that the line segment BC

is equal to the line segment AD.

• 1 month ago

Well, they are already given as congruent in the diagram so technically a proof is unnecessary.

If they weren't marked as congruent, you would say:

AB || CD --- Given

DB ≅ BD --- Reflexive property

∠ABD ≅ ∠CDB --- When a transversal (DB) cuts parallel lines, alternate interior angles are congruent.

△ADB ≅ △CBD --- ASA (angle-side-angle) triangle congruence postulate

BC ≅ AD --- Corresponding parts of congruent triangles are congruent (CPCTC)

Q.E.D.

• Anonymous
1 month ago

You have a parallelogram since by the alternate angle theorem, BC is parallel to AD.

Property of a parallelogram is that opposite sides are equal, so BC = AD