Question

Describe a single transformation that would map ∆ABC to ∆ADE.

Suppose AD = 5, AE = 4, DB = 10, and EC = 8. Find the scale factor that takes ∆ABC to ∆ADE. Explain how you calculate the scale factor and what your answer means.

Explain why ∆ABC and ∆ADE are similar.

Answer 1

To map ∆ABC to ∆ADE, we can use a scale factor of 1/2. ∆ABC and ∆ADE are similar triangles with congruent angles and proportional side lengths.

Step-by-step explanation:

To map ∆ABC to ∆ADE, we can use a scale factor to resize the triangle. The scale factor is determined by comparing corresponding side lengths of the two triangles. In this case, we can compare the length of AB to the length of AE, since they are corresponding sides. AB is 8 units long and AE is 4 units long. Therefore, the scale factor is 4/8, which simplifies to 1/2.

This means that we can resize ∆ABC by multiplying all the side lengths by 1/2 to obtain ∆ADE. For example, if the length of AC in ∆ABC is 6 units, then the length of AC in ∆ADE would be (1/2)*6 = 3 units.

∆ABC and ∆ADE are similar because their corresponding angles are congruent and their corresponding side lengths are proportional.