MNO has m<M=63 degrees and m<O=71 degrees. RST has m<R=58 degrees and m<T=71 degrees. applying the proof of the AA similarity theorem, is MNO~RST?

Question

no, they are not similar. m<N=46 degrees and m<S=51 degrees.

Yes m<N=~m<S=51 degrees.

n they are not similar. MN=/ RS

yes m<N=~m<S=46 degrees

Answer 1

To determine if triangles MNO and RST are similar using the AA (Angle-Angle) similarity theorem, we need to check the angles of both triangles.

1. Find angle N in triangle MNO:

   • The sum of the angles in a triangle is 180 degrees.
   • In triangle MNO, we have:
     • m<M = 63 degrees
     • m<O = 71 degrees
     • m<N = 180 - (63 + 71) = 180 - 134 = 46 degrees

2. Find angle S in triangle RST:

   • For triangle RST, we have:
     • m<R = 58 degrees
     • m<T = 71 degrees
     • m<S = 180 - (58 + 71) = 180 - 129 = 51 degrees

3. Comparing the angles of both triangles:

   • Triangle MNO has angles:
     • m<M = 63 degrees
     • m<O = 71 degrees
     • m<N = 46 degrees
   • Triangle RST has angles:
     • m<R = 58 degrees
     • m<T = 71 degrees
     • m<S = 51 degrees

Now we can observe the angle pairs:

• Compare m<M (63°) to m<R (58°) - not equal
• Compare m<O (71°) to m<T (71°) - equal
• Compare m<N (46°) to m<S (51°) - not equal

Since not all corresponding angles are equal, we can conclude that triangle MNO is not similar to triangle RST.

Therefore, the conclusion is: No, they are not similar.