Question

question 7 of 10
if \\( \triangle l m n \cong \triangle x y z \\), which congruences are true by cpctc? check all that apply.
\\( \square \\) a. \\( \angle x \cong \angle n \\)
\\( \square \\) b. \\( \angle y \cong \angle m \\)
\\( \square \\) c. \\( \overline{u n} \cong \overline{x z} \\)
\\( \square \\) d. \\( \angle z \cong \angle l \\)
\\( \square \\) e. \\( \overline{m l} \cong \overline{y x} \\)
\\( \square \\) f. \\( \overline{m n} \cong \overline{v x} \\)

Explanation:

CPCTC (Corresponding Parts of Congruent Triangles are Congruent) states that if two triangles are congruent, then their corresponding angles and sides are congruent.

• For angles:
• In \(\triangle LMN\cong\triangle XYZ\), \(\angle L\) corresponds to \(\angle X\), \(\angle M\) corresponds to \(\angle Y\), and \(\angle N\) corresponds to \(\angle Z\).
• For sides:
• \(\overline{LM}\) corresponds to \(\overline{XY}\), \(\overline{MN}\) corresponds to \(\overline{YZ}\), and \(\overline{LN}\) corresponds to \(\overline{XZ}\).

Answer:

B. \(\angle Y\cong\angle M\)
C. \(\overline{LN}\cong\overline{XZ}\)
E. \(\overline{ML}\cong\overline{YX}\)