Question

dc || ab
segment
db
is congruent to segment
bd
because they are the same segment. angles a and c are given to be congruent because they are both
degrees. since line dc and line ab are given to be , angle dba is congruent to angle bdc by
cbd is congruent to angle adb by
theorem. therefore, triangle abd is congruent to triangle cdb by
theorem.

Explanation:

Step1: Angle measure

Angles \(A\) and \(C\) are right - angles. So they are \(90\) degrees.

Step2: Parallel lines

Line \(DC\) and line \(AB\) are given to be parallel (\(DC\parallel AB\)).

Step3: Alternate interior angles

When two parallel lines (\(DC\) and \(AB\)) are cut by a transversal (\(DB\)), angle \(DBA\) is congruent to angle \(BDC\) by the Alternate Interior Angles Theorem.

Step4: Alternate interior angles

When two parallel lines (\(AD\) and \(BC\)) are cut by a transversal (\(DB\)), angle \(CBD\) is congruent to angle \(ADB\) by the Alternate Interior Angles Theorem.

Step5: Congruence of triangles

Since we have two pairs of congruent angles and a pair of congruent sides (\(DB = BD\) (common side)), triangle \(ABD\) is congruent to triangle \(CDB\) by the Angle - Angle - Side (\(AAS\)) Theorem.

Answer:

\(90\); parallel; Alternate Interior Angles; Alternate Interior Angles; \(AAS\)