Answer: SAS similarity postulate
Step-by-step explanation:
According to SAS postulate of similarity, two triangles are called similar if two sides in one triangle are in the same proportion to the corresponding sides in the other, and the included angle are congruent.
In triangles, QNR and MNP,
[tex]\frac{QN}{MN} = \frac{QM+MN}{MN} = \frac{10+8}{8} = \frac{18}{8} = \frac{9}{4}[/tex]
[tex]\frac{NR}{NP} = \frac{NP+NR}{NP} = \frac{10+8}{8} = \frac{18}{8} = \frac{9}{4}[/tex]
[tex]\implies \frac{QN}{MN} = \frac{NR}{NP}[/tex]
Also,
[tex]\angle QNR\cong \angle MNP[/tex] (Reflexive)
Thus, By SAS similarity postulate,
[tex]\triangle QNR\sim\triangle MNP[/tex]
⇒ Option first is correct.
