Answer:
Both triangles are similar by SAS
Step-by-step explanation:
See attachment for triangles
[tex]\triangle OKJ[/tex] and [tex]\triangle ONM[/tex]
From the attachment:
[tex]OK = 3; OJ = 30; KN = 1; JM = 3[/tex]
Calculate the lengths of ON and OM
[tex]ON=OK+KN=3+1= 4[/tex]
[tex]OM = OJ + JM = 30 + 10 = 40[/tex]
To determine if both triangles are similar or not, we make use of the following equivalent ratios
[tex]OK : OJ = ON : OM[/tex]
[tex]3 : 30 = 4 : 40[/tex]
Divide the first ratio by 3 and the second by 4
[tex]1:10 = 1 : 10[/tex] --- This implies that both triangles have 2 similar sides
From the attachment,
[tex]\angle KOJ = \angle NOM[/tex] ---- similar angles
Since the two triangles have 2 similar sides and a similar angle, then both triangles are similar by SAS
