Question

If ∆lmn ~= ∆xyz, which congruences are true by CPCTC?

Option 1: ∠l ≅ ∠x
Option 2: ∠m ≅ ∠z
Option 3: ∠l ≅ ∠m
Option 4: ∠n ≅ ∠y

Answer 1

By CPCTC, the congruences between ∆lmn and ∆xyz that are true are ∠l ≅ ∠x, ∠m ≅ ∠y, and ∠n ≅ ∠z. ∠l ≅ ∠m and ∠n ≅ ∠y are not correct as they do not correspond between the two triangles.

Step-by-step explanation:

If ∆lmn ~= ∆xyz, by CPCTC (Corresponding Parts of Congruent Triangles are Congruent), several congruences can be deduced:

1. ∠l ≅ ∠x: Since the triangles are congruent, their corresponding angles must be congruent.
2. ∠m ≅ ∠y: Again, corresponding angles in congruent triangles are congruent.
3. ∠n ≅ ∠z: This is also a set of corresponding angles that must be congruent.

However, ∠l ≅ ∠m is not necessarily true as they are angles within the same triangle and do not correspond to angles in the other triangle. Likewise, ∠n ≅ ∠y is incorrect for the same reason. Therefore, options 1, 2, and 4 are correct thanks to CPCTC, while option 3 is incorrect.