Let △ QTS and △ XWZ be a pair of triangles such that they are similar. Also, let TR and WY be angle bisectors.
Because corresponding angles of similar triangles are congruent, we have the following pair of congruences.
∠ T≅ ∠ W and ∠ Q ≅ ∠ X
⇓
m∠ T = m∠ W and m∠ Q = m∠ XBy the definition of an angle bisector we have that m∠ RTQ = 12m∠ T and m∠ YWX = 12m∠ W.
Given: & △ QTS ~ △ XWZ, TR and WY
& are angle bisectors
Prove: & TRWY = QTXW
We will summarize the proof we did above in the following two-column table.
