AB is three-fifths the length of AD and BC is three-fifths the length of DE. With the information given above, determine how triangle ABC can be shown to be similar to triangle ADE.

See explanation

Step-by-step explanation:

Given:

- AB = 3/5 * AD

- BC = 3/5 * DE

Find:

Determine how triangle ABC can be shown to be similar to triangle ADE.

Solution:

- The law of similar triangles states that all 3 angles must be similar:

AB / AD = BC / DE = AC / AE

- Then using the given data we will prove the above ratios to be equal:

(3/5) * AD / AD = (3/5) BC/BC = 3/5

- Now we know that angle A is common to both triangles ABC and ADE we have sum of angles:

A + B + C = A + D + E

B + C = D + E

- Since, angles B and D lie on parallel lines, the law of corresponding angle states that B = D. Hence,

E = C

- Hence, angle B = D, E = C and angle A is common to both. Proves that both ABC and ADE are similar triangles.