In △MNO , m∠M=78° , m∠N=34° , and m∠O=68° . In △RTS , m∠S=68° , m∠R=78° , and m∠T=34° . Describe the pairs of congruent corresponding angles in the two triangles

1 answer

To find the pairs of congruent corresponding angles in triangles \( \triangle MNO \) and \( \triangle RTS \), we will compare the measures of the angles in both triangles.

Given:

  • In \( \triangle MNO \):

    • \( m\angle M = 78^\circ \)
    • \( m\angle N = 34^\circ \)
    • \( m\angle O = 68^\circ \)
  • In \( \triangle RTS \):

    • \( m\angle S = 68^\circ \)
    • \( m\angle R = 78^\circ \)
    • \( m\angle T = 34^\circ \)

Now, let's match corresponding angles between the two triangles:

  1. \( m\angle M \) and \( m\angle R \):

    • \( m\angle M = 78^\circ \) and \( m\angle R = 78^\circ \)
    • These two angles are congruent: \( \angle M \cong \angle R \).
  2. \( m\angle N \) and \( m\angle T \):

    • \( m\angle N = 34^\circ \) and \( m\angle T = 34^\circ \)
    • These two angles are congruent: \( \angle N \cong \angle T \).
  3. \( m\angle O \) and \( m\angle S \):

    • \( m\angle O = 68^\circ \) and \( m\angle S = 68^\circ \)
    • These two angles are congruent: \( \angle O \cong \angle S \).

Conclusion: The pairs of congruent corresponding angles are:

  • \( \angle M \cong \angle R \)
  • \( \angle N \cong \angle T \)
  • \( \angle O \cong \angle S \)

This shows that the triangles are similar by the Angle-Angle (AA) similarity postulate, as they have pairs of congruent angles.