Question

Step 1: We know that ABC = ZFGH because all right angles
are congruent.
Step 2: We know that ZBAC = ZGFH because corresponding
angles of parallel lines are congruent.
Step 3: We know that BC =GH because it is given.
Step 4: ABC = AFGH because of the
O
ASA congruence theorem.
O AAS congruence theorem.
third angle theorem.
reflexive property.

Answer 1

The theorem that proves the congruency of ΔABC and FGH is obtained

from the given information on the triangles.

Correct response:

• ΔABC ≅ ΔFGH by; AAS congruency theorem

Which is the method by which the congruency of the triangles can be determined?

The given information are;

A two column proof is presented as follows;

Statement ${}$                                  Reason

∠ABC ≅ ∠FGH  ${}$                        All right angles are congruent

∠BAC ≅ ∠GFH ${}$                         Corresponding angles of parallel lines

BC = GH  ${}$                                   Given

Therefore;

ΔABC ≅ ΔFGH  ${}$                        AAS congruency theorem

The Angle-Angle-Side congruency theorem states that if two angles and

the non included side of one triangle are equal to the two angles and

the non included side of another triangle, then the two triangles are

congruent.

Learn more about AAS congruency postulate here:

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