Question

1. △ghi≅△kij 4.

blem 4:
statement\treason

1. ac∥bd,ab∥cd\t1. given
2. ∠1 = ∠4,∠2 = ∠3\t2.
3. ad≅ad\t3.
4. △adc≅△dab\t4.

choices for problems #1 - 4 (some will be used more than once):
aas
asa
alternate - interior angles are ≅
reflexive property
sas

Explanation:

Step1: Identify angle - equal reasons

Since \(AC\parallel BD\) and \(AB\parallel CD\), by the property of alternate - interior angles, when two parallel lines are intersected by a transversal, alternate - interior angles are equal. So, \(\angle1=\angle4\) and \(\angle2 = \angle3\) because alternate - interior angles are equal.

Step2: Identify side - equal reason

\(AD\cong AD\) by the reflexive property of congruence, which states that any segment is congruent to itself.

Step3: Identify triangle - congruence reason

In \(\triangle ADC\) and \(\triangle DAB\), we have \(\angle1=\angle4\), \(AD = AD\), and \(\angle2=\angle3\). By the Side - Angle - Side (SAS) congruence criterion (if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent), \(\triangle ADC\cong\triangle DAB\).

Answer:

1. Alternate Interior Angles are =
2. Reflexive Property
3. SAS