Question

The triangles below are similar. Triangle A B C. Side A C is 10 and side A B is 5. Angle C is 30 degrees. Triangle D E F. Side E D is 7.5 and side D F is 25. Angle F is 30 degrees and angle E is 90 degrees. Which similarity statements describe the relationship between the two triangles? Check all that apply.

Answer 1

a d and e on edg

Explanation:

Answer 2

`\triangle ABC {\displaystyle \sim } \triangle DE\ F`

`\triangle CBA {\displaystyle \sim } \triangle FED`

`\triangle BAC {\displaystyle \sim } \triangle EDF`

Explanation:

Given

`\triangle ABC {\displaystyle \sim } \triangle DE\ F`

`AC = 10`

`AB = 5`

`\angle C = 30^\circ`

`ED = 7.5`

`DF = 25`

`\angle F =30`

`\angle E =90`

Required

Which of the options is/are true:

`\triangle CBA {\displaystyle \sim } \triangle FED`
`\triangle CBA {\displaystyle \sim } \triangle FDE`
`\triangle BAC {\displaystyle \sim } \triangle EFD`

`\triangle BAC {\displaystyle \sim } \triangle EDF`
`\triangle ABC {\displaystyle \sim } \triangle DE\ F`
`\triangle ABC {\displaystyle \sim } \triangle DFE`

The given triangles, implies that:

`A {\displaystyle \sim } \ D`

`B {\displaystyle \sim } \ E`

`C {\displaystyle \sim } \ F`

By taking each sides of both triangle, one after the other; the possible similar triangles are:

`\triangle ABC {\displaystyle \sim } \triangle DE\ F`

`\triangle CBA {\displaystyle \sim } \triangle FED`

`\triangle BAC {\displaystyle \sim } \triangle EDF`