Answer:
The two column proof is presented as follows;
Statement [tex]{}[/tex] Reason
1. Parallelogram SUPN [tex]\overline {SR}[/tex]⊥ [tex]\overline {UN}[/tex] [tex]{}[/tex] 1. Given
and [tex]\overline {MP}[/tex]⊥ [tex]\overline {UN}[/tex]
2. ∠SRU = ∠PMN = 90° [tex]{}[/tex] 2. Definition of perpendicular lines
3. ∠SRU ≅ ∠PMN [tex]{}[/tex] 2. Definition of congruency
4. [tex]\overline {UP}[/tex] ║ [tex]\overline {SN}[/tex] [tex]{}[/tex] 4. Opposite sides of a parallelogram are [tex]{}[/tex] congruent
5. ∠SNR ≅ ∠PUM [tex]{}[/tex] 5. Alternate interior angles are congruent
6. [tex]\overline {UP}[/tex] ≅ [tex]\overline {SN}[/tex] [tex]{}[/tex] 6. Opposite sides of a parallelogram are [tex]{}[/tex] congruent
7. ΔPMU ≅ ΔSRN [tex]{}[/tex] 7. By AAS rule of congruency
By the Angle-Angle-Side (AAS) rule of congruency, we have that, if two angles and a corresponding adjacent side (∠SRU ≅ ∠PMN, ∠SNR ≅ ∠PUM, [tex]\overline {UP}[/tex] ≅ [tex]\overline {SN}[/tex]) of two triangles (ΔPMU and ΔSRN) are congruent, then the the two triangles are also congruent (ΔPMU ≅ ΔSRN)
Step-by-step explanation:
