Two triangles are sketched on a coordinate plane using a dilation of 2, sharing the same center ordered pair at the origin. one triangle has angle measures of 34 degrees and 80 degrees. using the AA criterion, what would be the two corresponding angles of the dilated triangle.

1 answer

When a triangle is dilated, the angles of the triangle do not change. The AA (Angle-Angle) criterion states that if two triangles have two angles that are congruent, then the triangles are similar.

Since the triangle with angle measures of 34 degrees and 80 degrees has a third angle that can be calculated as follows:

\[ \text{Third angle} = 180^\circ - (34^\circ + 80^\circ) = 180^\circ - 114^\circ = 66^\circ \]

The angles of the original triangle are 34 degrees, 80 degrees, and 66 degrees. After applying a dilation of 2 centered at the origin, the dilated triangle will have the same angle measures.

Thus, the two corresponding angles of the dilated triangle will also be:

  • 34 degrees
  • 80 degrees

And the third angle will remain as 66 degrees. So, the corresponding angles of the dilated triangle are 34 degrees, 80 degrees, and 66 degrees.