Answered

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Given: AD
= BC and AD
•BC
Prove: ABCD is a parallelogram.
Angles
Segments
LBCA
Triangles
Statements
Reasons
LDAC
Statements
Reasons
C
Assemble the proof by dragging tiles to the Statements and Reasons columns.

Sagot :

anuradhadevi1937

[tex]

\text{Given:} \\

AD = BC \quad \text{and} \quad AD \parallel BC \\

\text{To Prove:} \\

ABCD \text{ is a parallelogram.} \\

\text{Proof:} \\

\begin{array}{ll}

1. & AD = BC \quad \text{(Given)} \\

2. & AD \parallel BC \quad \text{(Given)} \\

3. & \angle DAC = \angle ACB \quad \text{(Alternate Interior Angles Theorem)} \\

4. & \angle DCA = \angle BAC \quad \text{(Alternate Interior Angles Theorem)} \\

5. & \triangle DAC \cong \triangle ACB \quad \text{(SAS Congruence Postulate)} \\

6. & AB \parallel CD \quad \text{(Corresponding Angles Postulate from congruent triangles)} \\

7. & \text{ABCD is a parallelogram} \quad \text{(Opposite sides are equal and parallel)}

\end{array}

[/tex]

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