Question

the triangles below are congruent and their corresponding parts are
name all the corresponding congruent angles and sides.
then, complete the triangle congruence statement.
(a) ( angle a cong angle square )
( angle b cong angle square )
(b) ( overline{ab} cong overline{square} )
( overline{ac} cong overline{square} )

Explanation:

Step1: Identify corresponding angles

In congruent triangles, angles with the same markings correspond. In \(\triangle ABC\) and \(\triangle XYZ\), \(\angle A\) (with one - arc marking) corresponds to \(\angle Z\) (with one - arc marking in \(\triangle XYZ\)), and \(\angle B\) (with no - arc marking in \(\triangle ABC\)) corresponds to \(\angle Y\) (with no - arc marking in \(\triangle XYZ\)).

Step2: Identify corresponding sides

Sides with the same number of tick - marks correspond. \(\overline{AB}\) (with two - tick marks) corresponds to \(\overline{YZ}\) (with two - tick marks in \(\triangle XYZ\)), and \(\overline{AC}\) (with one - tick mark) corresponds to \(\overline{XZ}\) (with one - tick mark in \(\triangle XYZ\)).

Answer:

(a) \(\angle A\cong\angle Z\), \(\angle B\cong\angle Y\)
(b) \(\overline{AB}\cong\overline{YZ}\), \(\overline{AC}\cong\overline{XZ}\)