Question

A sequence of transformations which moves Δlmn onto Δopq shows that Δlmn ≅ Δopq. Which part of the triangles are congruent by CPCTC?

1) ∠n ≅ ∠o
2) ∠m ≅ ∠p
3) ∠l ≅ ∠q
4) ∠o ≅ ∠m

Answer 1

Using CPCTC, the correct congruent angles between Δlmn and Δopq are such that ∠m is congruent to ∠p based on the naming of the vertices in the congruence statement.

Step-by-step explanation:

When using the concept of Congruent Parts of Congruent Triangles are Congruent (CPCTC), we can determine which angles of the given congruent triangles are also congruent to one another. The angle correspondence is based on the naming of the vertices of the triangles. For instance, if Δlmn is moved onto Δopq, then each angle in Δlmn would correspond to a congruent angle in Δopq based on the order of the vertices in the given congruence statement. Therefore:

1. ∠m corresponds to ∠p
2. ∠n corresponds to ∠q

Among the options provided, the correct pairing by CPCTC is ∠m ≅ ∠p, as these are the corresponding angles when Δlmn is congruent to Δopq.