Answer:
See explanation
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.