Question

question 10 (1 point)
show that the polygons are congruent by identifying all congruent corresponding parts. then write a congruence statement.
○ a △abc ≅ △rds
∠a ≅ ∠r, ∠b ≅ ∠d, ∠c ≅ ∠s;
overline{ab} ≅ overline{rd}, overline{bc} ≅ overline{ds}, overline{ac} ≅ overline{rs};
○ b △abc ≅ △srd
∠a ≅ ∠s, ∠b ≅ ∠r, ∠c ≅ ∠d;
overline{ab} ≅ overline{sr}, overline{bc} ≅ overline{rd}, overline{ac} ≅ overline{sd};
○ c △abc ≅ △drs
∠a ≅ ∠d, ∠b ≅ ∠r, ∠c ≅ ∠s;
overline{ab} ≅ overline{dr}, overline{bc} ≅ overline{rs}, overline{ac} ≅ overline{ds};
○ d △abc ≅ △dsr
∠a ≅ ∠d, ∠b ≅ ∠s, ∠c ≅ ∠r;
overline{ab} ≅ overline{ds}, overline{bc} ≅ overline{sr}, overline{ac} ≅ overline{dr}.

Explanation:

Step1: Identify corresponding parts

In congruent triangles, corresponding angles and sides are equal. For \(\triangle ABC\) and \(\triangle RDS\), when \(\angle A\cong\angle R\), \(\angle B\cong\angle D\), \(\angle C\cong\angle S\), then \(\overline{AB}\cong\overline{RD}\), \(\overline{BC}\cong\overline{DS}\), \(\overline{AC}\cong\overline{RS}\)

Answer:

a. \(\triangle ABC\cong\triangle RDS\)