Question

given: ∠abc and ∠fgh are right angles; (overline{ba}paralleloverline{gf}); (overline{bc}congoverline{gh}) prove: (\triangle abccong\triangle 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 (overline{bc}congoverline{gh}) because it is given. step 4: (\triangle abccong\triangle fgh) because of the reflexive property. third angle theorem. asa congruence theorem. aas congruence theorem.

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

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

Step4: Triangle - congruence determination

We have two pairs of congruent angles and the included side between them is congruent. By the ASA (Angle - Side - Angle) congruence theorem, $\triangle ABC\cong\triangle FGH$.

Answer:

ASA congruence theorem