Question

given:
prove:
1
2
3
4
5
arrange the cards to
complete the proof.
mark sets of congruent sides and angles if
the corresponding congruence statement
is justified in the proof.

Explanation:

Step1: Identify congruent angles from parallel lines

Since \(\overline{AB}\parallel\overline{DC}\), by the Alternate Interior Angles Theorem, \(\angle DBA\cong\angle BDC\).

Step2: Identify another set of congruent angles from parallel lines

Since \(\overline{AD}\parallel\overline{CB}\), by the Alternate Interior Angles Theorem, \(\angle ADB\cong\angle CBD\).

Step3: Identify the common side

\(\overline{BD}\cong\overline{BD}\) (Reflexive Property of Congruence).

Step4: Prove triangle congruence

By the ASA (Angle - Side - Angle) Triangle Congruence Theorem, \(\triangle ADB\cong\triangle CBD\).

Step5: Conclude the proof

By CPCTC (Corresponding Parts of Congruent Triangles are Congruent), \(\overline{AB}\cong\overline{CB}\).

Answer:

1. \(\angle DBA\cong\angle BDC\) (Alternate Interior angles are congruent)
2. \(\angle ADB\cong\angle CBD\) (Alternate Interior angles are congruent)
3. \(\overline{BD}\cong\overline{BD}\)
4. \(\triangle ADB\cong\triangle CBD\) (ASA triangle congruence theorem)
5. \(\overline{AB}\cong\overline{CB}\) (CPCTC)