Answer:
[tex]\triangle ABC {\displaystyle \sim } \triangle DE\ F[/tex]
[tex]\triangle CBA {\displaystyle \sim } \triangle FED[/tex]
[tex]\triangle BAC {\displaystyle \sim } \triangle EDF[/tex]
Step-by-step explanation:
Given
[tex]\triangle ABC {\displaystyle \sim } \triangle DE\ F[/tex]
[tex]AC = 10[/tex]
[tex]AB = 5[/tex]
[tex]\angle C = 30^\circ[/tex]
[tex]ED = 7.5[/tex]
[tex]DF = 25[/tex]
[tex]\angle F =30[/tex]
[tex]\angle E =90[/tex]
Required
Which of the options is/are true:
[tex]\triangle CBA {\displaystyle \sim } \triangle FED[/tex] [tex]\triangle CBA {\displaystyle \sim } \triangle FDE[/tex] [tex]\triangle BAC {\displaystyle \sim } \triangle EFD[/tex]
[tex]\triangle BAC {\displaystyle \sim } \triangle EDF[/tex] [tex]\triangle ABC {\displaystyle \sim } \triangle DE\ F[/tex] [tex]\triangle ABC {\displaystyle \sim } \triangle DFE[/tex]
The given triangles, implies that:
[tex]A {\displaystyle \sim } \ D[/tex]
[tex]B {\displaystyle \sim } \ E[/tex]
[tex]C {\displaystyle \sim } \ F[/tex]
By taking each sides of both triangle, one after the other; the possible similar triangles are:
[tex]\triangle ABC {\displaystyle \sim } \triangle DE\ F[/tex]
[tex]\triangle CBA {\displaystyle \sim } \triangle FED[/tex]
[tex]\triangle BAC {\displaystyle \sim } \triangle EDF[/tex]
