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Answer:
B. Vanessa only established some of the necessary conditions for a congruence criterion.
Step-by-step explanation:
The diagram does support the claim that \overline{KL}\cong\overline{MN}
KL
≅
MN
start overline, K, L, end overline, \cong, start overline, M, N, end overline because they both have two tick marks.
Step 1 is correct.
Step 2
The diagram does support the claim that \overline{LM}\cong\overline{NK}
LM
≅
NK
start overline, L, M, end overline, \cong, start overline, N, K, end overline because they both have a single tick mark.
Step 2 is correct.
Step 3
In this step, Vanessa claims that \triangle KLM\cong \triangle MNK△KLM≅△MNKtriangle, K, L, M, \cong, triangle, M, N, K using the side-side-side criterion. But Vanessa only established two pairs of congruent corresponding sides. To use this criterion, we must establish three pairs of congruent sides.
Vanessa would be able to use this criterion if she first established that \overline{MK}\cong\overline{KM}
MK
≅
KM
start overline, M, K, end overline, \cong, start overline, K, M, end overline (this can be done with the reason that line segments are congruent to themselves).
The first error Vanessa made in her proof was option B.
Vanessa only established two pairs of congruent corresponding sides
polygons are congruent if they may be identical in size and shape - that is, if their corresponding angles and sides are the same.
Congruent shapes are shapes that can be exactly equal. The corresponding facets are identical and the corresponding angles are equal.
⇒KL≅ MN 9K, L, end overline)
⇒LM≅ NK
⇒MNK△KLM≅△MNK (triangle, K, L, M)
Vanessa would be able to use this criterion if she first established that
⇒MK≅ KM
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