Question

Verify that △ABC∼△DEF. Find the scale factor of △ABC to △DEF.

△ABC: AB = 10, BC = 16, CA = 20
△DEF: DE = 25, EF = 40, FD = 50
I really need someone to explain to me how to do this because i am so confused my teacher didn't give us notes and didn't explain this very well.

Answer 1

To verify if △ABC is similar to △DEF the sides are compared and found to be proportional with a ratio of 2/5. Therefore, △ABC≈△DEF and the scale factor is 2:5.

Step-by-step explanation:

To verify whether △ABC≈△DEF, we need to check if the sides of △ABC are proportional to the sides of △DEF. We are given:

• AB = 10, BC = 16, CA = 20
• DE = 25, EF = 40, FD = 50

We can now compare the corresponding sides of △ABC and △DEF to determine if the triangles are similar and find the scale factor. For triangles to be similar by the SSS (Side-Side-Side) similarity criterion, the ratio of corresponding sides must be the same:

AB/DE = BC/EF = CA/FD

Let's do the calculations:

• AB/DE = 10/25 = 2/5
• BC/EF = 16/40 = 2/5
• CA/FD = 20/50 = 2/5

Since all the side ratios are identical (2/5), △ABC is similar to △DEF and the scale factor from △ABC to △DEF is 2:5 (or 2/5 as a fraction).

Answer 2

2/3 i got it right

Step-by-step explanation: