Question

show that the polygons are congruent by identifying all the congruent corresponding parts. then complete the congruence statement.

∠a ≅ ∠select choice;
∠abc ≅ ∠select choice;
∠acb ≅ ∠select choice;
segment ac ≅ segment select choice;
segment ab ≅ segment select choice;
△abc ≅ △select choice

Explanation:

Step1: Identify congruent angles

By observing the figure, \(\angle A\) and \(\angle D\) are congruent.

Step2: Identify congruent angles

\(\angle ABC\) and \(\angle DCB\) are congruent.

Step3: Identify congruent angles

\(\angle ACB\) and \(\angle DBC\) are congruent.

Step4: Identify congruent segments

Segment \(AC\) and segment \(DB\) are congruent.

Step5: Identify congruent segments

Segment \(AB\) and segment \(CD\) are congruent.

Step6: Determine congruent triangles

Since all corresponding parts are congruent, \(\triangle ABC\cong\triangle CDB\)

Answer:

\(\angle A\cong\angle D\); \(\angle ABC\cong\angle DCB\); \(\angle ACB\cong\angle DBC\); segment \(AC\cong\) segment \(DB\); segment \(AB\cong\) segment \(CD\); \(\triangle ABC\cong\triangle CDB\)