in the figure below, the two triangles are similar.
be corresponds to (da/ dn/ an)
en corresponds to (da/ dn/ an)
bn corresponds to (da/ dn/ an)
what is the scale factor applied to △ben to achieve △dan?
what is the scale factor applied to △dan to achieve △ben?

Question

Accepted Answer

### 1. BE corresponds to which side?
# Brief Explanations:
In similar triangles $ \triangle BEN $ and $ \triangle DAN $, we match sides by their positions. $ BE $ is a side of $ \triangle BEN $, and $ DA $ is the corresponding side in $ \triangle DAN $ as they are the "outer" sides of each triangle (not adjacent to the common vertex $ N $). Also, checking lengths: $ BE = 6 $, $ DA = 3 $, and $ 6/3 = 2 $, which is consistent with similarity. So $ BE $ corresponds to $ DA $.
# Answer: DA

### 2. EN corresponds to which side?
# Brief Explanations:
$ EN $ is a side of $ \triangle BEN $ (length 8), and in $ \triangle DAN $, $ AN $ is the corresponding side (length 4). The ratio $ 8/4 = 2 $, which fits the similarity. Also, by the structure of the triangles (base sides from $ N $ to $ E $ and $ N $ to $ A $), $ EN $ corresponds to $ AN $.
# Answer: AN

### 3. BN corresponds to which side?
# Brief Explanations:
$ BN $ is a side of $ \triangle BEN $ (length 7), and in $ \triangle DAN $, $ DN $ is the corresponding side (length 3.5). The ratio $ 7/3.5 = 2 $, consistent with similarity. By the triangle structure (sides from $ B $ and $ D $ to $ N $), $ BN $ corresponds to $ DN $.
# Answer: DN

### 4. Scale factor from $ \triangle BEN $ to $ \triangle DAN $
# Explanation:
## Step1: Identify corresponding sides
Take $ BE = 6 $ (from $ \triangle BEN $) and $ DA = 3 $ (from $ \triangle DAN $).
## Step2: Calculate the ratio
Scale factor $ = \frac{\text{Length in } \triangle DAN}{\text{Length in } \triangle BEN} = \frac{3}{6} = \frac{1}{2} $ (or using other corresponding sides: $ \frac{4}{8} = \frac{1}{2} $, $ \frac{3.5}{7} = \frac{1}{2} $).
# Answer: $ \frac{1}{2} $

### 5. Scale factor from $ \triangle DAN $ to $ \triangle BEN $
# Explanation:
## Step1: Identify corresponding sides
Take $ DA = 3 $ (from $ \triangle DAN $) and $ BE = 6 $ (from $ \triangle BEN $).
## Step2: Calculate the ratio
Scale factor $ = \frac{\text{Length in } \triangle BEN}{\text{Length in } \triangle DAN} = \frac{6}{3} = 2 $ (or using other sides: $ \frac{8}{4} = 2 $, $ \frac{7}{3.5} = 2 $).
# Answer: $ 2 $

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QUESTION IMAGE

Question

Explanation:

1. BE corresponds to which side?

Answer:

2. EN corresponds to which side?