Given: AD = BC and AD || BC
Prove: ABCD is a parallelogram.
Angles Segments Triangles Statements Reasons
ZBCA
DAC
A
Statements
Reasons
00
D
с
Assemble the proof by dragging tiles to
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ujalakhan18 ujalakhan18 · Answer 1 · 2020-07-22T02:46:59+02:00

Answer:

See below

Step-by-step explanation:

Proof:

Statements | Reasons

AD ≅ BC | Given

AD ║ BC | Given

AC ≅ AC | Reflexive Property

∠DAC ≅ ∠ACB | If 2 || lines are cut by a trans., the | alternate interior ∠s are congruent.

ΔADC ≅ ΔBCA | S.A.S Postulate

BA ≅ DC | Corresponding sides of congruent Δs

So, quad. ABCD is a ║gm | If a quad. has its opposite sides

| congruent, the quad. is a parallelogram.

ibiscollingwood ibiscollingwood · Answer 2 · 2022-02-03T14:11:32+01:00

It is prove that given quadrilateral is a parallelogram.

AD ≅ BC and AD ║ BC

AC ≅ AC

If two parallel lines are cut by a transversal. Then, alternate interior angles are congruent.

So that, ∠DAC ≅ ∠ACB

ΔADC ≅ ΔBCA

So that, BA ≅ DC

Hence, opposite sides of given quadrilateral are equal. Therefore, given quadrilateral are parallelogram.

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