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 (∠abccong∠fgh) because all right angles are congruent. step 2: we know that (∠baccong∠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 asa congruence theorem. aas congruence theorem. third angle theorem. reflexive property.

Explanation:

Step 1: Identify congruent angles and side

• We have two angles ($\angle ABC\cong\angle FGH$, $\angle BAC\cong\angle GFH$) and a non - included side ($BC\cong GH$).

Step 2: Recall congruence theorems

• The ASA (Angle - Side - Angle) theorem requires the side to be included between the two angles.
• The AAS (Angle - Angle - Side) theorem is for two angles and a non - included side.
• The third angle theorem just states that if two angles of one triangle are congruent to two angles of another triangle, the third angles are congruent. It is not a congruence theorem.
• The reflexive property is about a figure being congruent to itself ($a\cong a$).

Answer:

AAS congruence theorem.