Question

given: ∠abc and ∠fgh are right angles; ba||gf; bc≅gh
prove: △abc≅△fgh
step 1: we know that ∠abc≅∠fgh because all right angles are congruent.
step 2: we know that ∠bac≅∠gfh because corresponding angles of parallel lines are congruent.
step 3: we know that bc≅gh because it is given.
step 4: △abc≅△fgh because of the
○ asa congruence theorem.
○ aas congruence theorem.
○ third angle theorem.
○ reflexive property.

Explanation:

Step1: Right - angle congruence

All right angles are congruent, so $\angle ABC\cong\angle FGH$.

Step2: Corresponding - angle congruence

Since $\overline{BA}\parallel\overline{GF}$, corresponding angles $\angle BAC\cong\angle GFH$.

Step3: Given side - congruence

It is given that $\overline{BC}\cong\overline{GH}$.

Step4: Triangle - congruence determination

We have two pairs of congruent angles and a pair of congruent non - included sides. By the AAS (Angle - Angle - Side) congruence theorem, $\triangle ABC\cong\triangle FGH$.

Answer:

AAS congruence theorem.