The missing steps are each right angles and [tex]\angle R \cong \angle O[/tex].
Solution:
Step 1: Given data:
[tex]\overline {P Q} \cong \overline{M N}[/tex]
[tex]\overline{Q R} \cong \overline{N O}[/tex]
[tex]\overline{P R} \cong \overline{M O}[/tex]
Step 2: In the two polygons,
[tex]\angle Q =90^\circ[/tex] and [tex]\angle N =90^\circ[/tex]
[tex]\angle Q \cong \angle N[/tex] (Each right angle)
Step 3: Given
[tex]\angle P \cong \angle M[/tex]
Step 4: By third angle theorem,
If two angles in one triangle are congruent to the two angles in the other triangle, then the third angles in the triangles also congruent.
[tex]\angle R \cong \angle O[/tex]
Step 5: By the definition of congruent polygons,
If two same shape polygons have all the angles are congruent and all the corresponding sides are congruent then the polygons are congruent.
Hence [tex]\Delta P Q R \cong \Delta M N O[/tex].
Therefore the missing steps are each right angles and [tex]\angle R \cong \angle O[/tex].
