Question

Which triangle is ​△MNO​ similar to and why? △MNO is similar to △GHK by ​ AA Similarity Postulate ​. ​△MNO​ is similar to △DEF by ​ ​ AA Similarity Postulate ​. △MNO is similar to △PQR by ​ ​ AA Similarity Postulate ​. ​△MNO​ is not similar to any of the triangles given. NOTE: Figures are not drawn to scale. Four triangles of different sizes. Triangle N M O has angle N M O measuring seventy-nine degrees and angle M O N measuring twenty-two degrees. Triangle G H K has angle H G K measuring seventy-nine degrees and angle H G K measuring seventy-nine degrees. Triangle P Q R has angle P R Q measuring twenty degrees and angle R Q P measuring seventy-nine degrees. Triangle D E F has angle D E F measuring eighty-two degrees and angle D F E measuring twenty-two degrees.\

Answer 1

MNO is similar to GHK by AA Similarity Postulate

   Let's start by listing each triangle and the measurements of all three angles. For each triangle, we've been given the measurements of 2 of the angles and the 3 angle will simply be 180 minus the other 2 angles. I assume you can do the subtraction, so I'll simply list each triangle with all three angle measurements.
 NMO: 79, 22, 79
 GHK: 79, 79, 22
 PQR: 20, 79, 81
 DEF: 82, 22, 76
   And the triangles NMO and GHK are similar to each other since they have the same angles. The order really doesn't matter since it's OK for similar triangles to be rotated or reflected. The key thing to remember in a triangle is that if you've been told what 2 of the angles are, you also know what the 3rd angle is since the sum of the angles of a triangle will always be 180.
So the answer is:
 MNO is similar to GHK by AA Similarity Postulate"