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QUESTION IMAGE

complete the congruence statements requested using the given informatio…

Question

complete the congruence statements requested using the given information.
given: ( colncong bake )
( overline{co}cong )____ ( overline{ek}cong )__ ( overline{lo}cong )__ ( overline{be}cong )____
( angle lcong )____ ( angle kabcong )__ ( angle bcong )__ ( angle cnlcong )____

Explanation:

Step1: Identify corresponding parts

When two polygons are congruent, their corresponding sides and angles are congruent. For \(COLN\cong BAKE\), the order of the letters gives the correspondence. \(C\) corresponds to \(B\), \(O\) corresponds to \(A\), \(L\) corresponds to \(K\), \(N\) corresponds to \(E\).

Step2: Find congruent sides

  • For \(\overline{CO}\), since \(C\) corresponds to \(B\) and \(O\) corresponds to \(A\), \(\overline{CO}\cong\overline{BA}\)
  • For \(\overline{EK}\), since \(E\) corresponds to \(N\) and \(K\) corresponds to \(L\), \(\overline{EK}\cong\overline{NL}\)
  • For \(\overline{LO}\), since \(L\) corresponds to \(K\) and \(O\) corresponds to \(A\), \(\overline{LO}\cong\overline{KA}\)
  • For \(\overline{BE}\), since \(B\) corresponds to \(C\) and \(E\) corresponds to \(N\), \(\overline{BE}\cong\overline{CN}\)

Step3: Find congruent angles

  • For \(\angle L\), since \(L\) corresponds to \(K\), \(\angle L\cong\angle K\)
  • For \(\angle KAB\), since \(K\) corresponds to \(L\), \(A\) corresponds to \(O\), \(B\) corresponds to \(C\), \(\angle KAB\cong\angle LOC\)
  • For \(\angle B\), since \(B\) corresponds to \(C\), \(\angle B\cong\angle C\)
  • For \(\angle CNL\), since \(C\) corresponds to \(B\), \(N\) corresponds to \(E\), \(L\) corresponds to \(K\), \(\angle CNL\cong\angle BEK\)

Answer:

\(\overline{CO}\cong\overline{BA}\), \(\overline{EK}\cong\overline{NL}\), \(\overline{LO}\cong\overline{KA}\), \(\overline{BE}\cong\overline{CN}\), \(\angle L\cong\angle K\), \(\angle KAB\cong\angle LOC\), \(\angle B\cong\angle C\), \(\angle CNL\cong\angle BEK\)