What is the scale factor for the similar triangles? Choose all that apply.

Question

Similar triangles; larger triangle has side lengths 2 and 8; smaller triangles has corresponding side lengths 1.5 and 6

Multiple select question.

12


23


34


2


32


43

Answer 1

To find the scale factor for similar triangles, we compare corresponding side lengths.

For the larger triangle:

• One side length is 2, and the corresponding side length in the smaller triangle is 1.5.
• For the second side length, the larger triangle is 8, and the smaller triangle has the side length of 6.

Now, we calculate the scale factor for each pair of corresponding sides:

1. From side length 2 to side length 1.5: \[ \text{Scale factor} = \frac{\text{Larger side}}{\text{Smaller side}} = \frac{2}{1.5} = \frac{2 \times 2}{1.5 \times 2} = \frac{4}{3} \approx 1.33 \]

2. From side length 8 to side length 6: \[ \text{Scale factor} = \frac{\text{Larger side}}{\text{Smaller side}} = \frac{8}{6} = \frac{8 \div 2}{6 \div 2} = \frac{4}{3} \approx 1.33 \]

Both corresponding side pairs yield a scale factor of \(\frac{4}{3}\).

Since the scale factor is consistent between the pairs, the scale factor for these similar triangles is \(\frac{4}{3}\).

Thus, the scale factor is \(\frac{4}{3}\).

Among the options provided, the only applicable scale factor is:

• 43 (which represents \(\frac{4}{3}\)).

The others do not apply to the calculated scale factor.

Answer 2

Which proportion is correct for the similar triangles if △ABC~△DEF
? Choose the correct answer.

Similar Triangles ABC and DEF

Multiple choice question.

ABAC=DEDF


BCAC=EFDE


ACAB=EFDE


BCAB=DFDE

Answer 3

For similar triangles \( \triangle ABC \sim \triangle DEF \), the proportions of the corresponding sides should be set equal to each other. The correct relationship can generally be expressed as follows:

\[ \frac{AB}{DE} = \frac{BC}{EF} = \frac{AC}{DF} \]

Now let's assess each of the provided options:

1. \( \frac{AB}{AC} = \frac{DE}{DF} \)
   This is not correct because the denominators and numerators do not correspond to the correct side pairs.

2. \( \frac{BC}{AC} = \frac{EF}{DE} \)
   This is also incorrect; again, the correspondences do not match.

3. \( \frac{AC}{AB} = \frac{EF}{DE} \)
   This does not match the ratios of corresponding sides.

4. \( \frac{BC}{AB} = \frac{DF}{DE} \)
   This is incorrect for similar triangles as the sides do not correspond correctly.

Given the presented options, unfortunately, none of the proportion options provided represents the correct relationships for the similar triangles \( \triangle ABC \sim \triangle DEF \).

Ideally, the correct proportions would be:

\[ \frac{AB}{DE} = \frac{BC}{EF} = \frac{AC}{DF} \]

If none of the options provide the correct proportions, it's best to consult the problem context or consider potential typos.