PLEASE ANSWER THE QUESTION

Question

Which statement is true?

1. 
   
2. A.
3. m∠LOM < m∠NOM
4. 
   
5. B.
6. ∠MLO ≅ ∠LMO
7. 
   
8. C.
9. ∠MLO ≅ ∠NMO
10. 
    
11. D.
12. The circumcenter of each triangle is located outside the triangle.

Answer 1

Hinge Theorem:

For two triangles with two equal sides, the angle opposite the larger non-equal side is larger than the angle opposite the smaller non-equal side, so A cannot be true because <LOM is opposite a bigger side than <NOM.

Isosceles triangle:

If two sides of a triangle are equal, then the angles opposite those sides are equal. <MLO and <LMO are both opposite sides of equal length (9), so B is true.

C is not true, because just because angles are opposite sides of equal length in two different triangles it doesn't mean those angles are equal.

The circumcenter of a triangle will lie outside the triangle if it is an obtuse triangle. Both triangles are acute isosceles triangles, do D is not true.