ΔMNO has m∠M=63 degrees and m∠O=71 degrees. ΔRST has m∠R=58 degrees and m∠T=71 degrees. Applying the proof of the AA Similarity Theorem, is △MNO∼△RST ?(1 point)

Question

Responses

No, they are not similar. MN≠RS .
No, they are not similar. MN≠RS .

No, they are not similar. m∠N=46 degrees and m∠S=51 degrees
No, they are not similar. m∠N=46 degrees and m∠S=51 degrees

Yes, m∠N≅m∠S=51 degrees.
Yes, m∠N≅m∠S=51 degrees.

Yes, m∠N≅m∠S=46 degrees.

Answer 1

To determine if the triangles ΔMNO and ΔRST are similar using the AA (Angle-Angle) Similarity Theorem, we need to check if the corresponding angles are equal.

1. For triangle ΔMNO:

   • m∠M = 63 degrees
   • m∠O = 71 degrees
   • To find m∠N, we can use the fact that the sum of angles in a triangle is 180 degrees.
   • m∠N = 180 - (m∠M + m∠O) = 180 - (63 + 71) = 180 - 134 = 46 degrees.

2. For triangle ΔRST:

   • m∠R = 58 degrees
   • m∠T = 71 degrees
   • To find m∠S, we calculate similarly:
   • m∠S = 180 - (m∠R + m∠T) = 180 - (58 + 71) = 180 - 129 = 51 degrees.

Now we compare the angles:

• ΔMNO has angles of 63 degrees, 71 degrees, and 46 degrees.
• ΔRST has angles of 58 degrees, 71 degrees, and 51 degrees.

The triangles share the angle of 71 degrees, but the other angles are not equal (m∠N = 46 degrees is not equal to m∠S = 51 degrees).

Since we found that the triangles do not have all corresponding angles equal, we conclude that:

No, they are not similar. m∠N=46 degrees and m∠S=51 degrees.