Question

If ΔMNO ≅ ΔXYZ, then what corresponding parts are congruent?

∠M and ∠Z
segment MN and segment ZX
∠N and ∠Y
segment NO and segment YX

Answer 1

If ∆MNO ≅ ∆XYZ, then ∠M corresponds to ∠X, ∠N corresponds to ∠Y, and ∠O corresponds to ∠Z. Sides MN, NO, and OM correspond to sides XY, YZ, and XZ, respectively. The order of lettering in the triangle names dictates the correspondence.

Step-by-step explanation:

If ∆MNO ≅ ∆XYZ, then by the definition of congruent triangles, corresponding parts of these triangles are congruent. This means that each angle or side in one triangle has a corresponding equal angle or side in the other triangle. Specifically:

∠M is congruent to ∠X

Segment MN is congruent to segment XY

∠N is congruent to ∠Y

Segment NO is congruent to segment YZ

Note that the congruence of angles and sides follows the order of the letters in the names of the triangles. This means that the first letter in ∆MNO corresponds to the first letter in ∆XYZ (∠M to ∠X), the second to the second (∠N to ∠Y), and the third to the third (∠O to ∠Z). The same pattern follows for the sides of the triangles. Therefore, in the question's choices, the correct pairs are ∠N and ∠Y, and segment NO and segment YZ.