Question

If lmn xyz, which congruences are true by CPCTC? Check all that apply.

a. ∠b ≅ ∠x
b. ∠n ≅ ∠c
c. ∠y ≅ ∠m
d. ∠z ≅ ∠l
e. ∠f ≅ ∠e

Answer 1

The correct answer is option c. In the context of triangle △LMN being congruent to △XYZ, the only CPCTC congruence from the listed options is c. ∠y ≡ ∠m, as it correctly matches corresponding angles between the congruent triangles.

Step-by-step explanation:

The question refers to identifying congruent angles in corresponding triangles using the principle of CPCTC (Corresponding Parts of Congruent Triangles are Congruent), which states that if two or more triangles are proven to be congruent, then all of their corresponding angles and sides are congruent as well. The notation 'lmn xyz' suggests that triangle △LMN is congruent to triangle △XYZ. Hence, by CPCTC, corresponding angles of these triangles would be congruent:

• ∠l ≡ ∠x
• ∠m ≡ ∠y
• ∠n ≡ ∠z

Therefore, the congruences that are true by CPCTC must match with the corresponding angles of the triangles given. Checking against the options:

• b. ∠n ≡ ∠c is not true because there is no angle 'c' corresponding to angle 'n' in the congruent triangle.
• c. ∠y ≡ ∠m is true because angle 'y' corresponds to angle 'm' in the congruent triangle.
• d. ∠z ≡ ∠l is not true because angle 'z' corresponds to angle 'n', not angle 'l'.

In summary, among the options given, the only valid CPCTC congruence is c. ∠y ≡ ∠m.