In the given figure ∆ABC~∆DEF AP bisects ∠CAB and DQ bisects ∠FDE Prove that (a) - Maths - Real Numbers

Question

In the given figure ∆ A B C ~ ∆ D E F AP bisects
∠ C A B and DQ bisects ∠ F D E

Prove that
(a) A P D Q = A B D E
(b) ∆ C A P ~ ∆ F D Q

Manbar Singh · Accepted Answer

Since, ∆ABC~∆DEF, then∠A = ∠D; ∠B = ∠E; ∠C = ∠FSince, AP bisects ∠CAB, then∠CAP = ∠PAB = 12∠ASince, DQ bisects ∠FDE, then∠FDQ = ∠QDE = 12∠DNow, ∠A = ∠B  Given⇒12∠A = 12∠D⇒∠CAP = ∠FDQ and ∠PAB = ∠DQE    
1In ∆PAB and ∆QDE∠PAB = ∠DQE  Using 1∠B = ∠C   Given⇒∆PAB ~ ∆QDE  AA⇒PAQD = ABDE = PBQE  Corresponding sides of similar ∆'s are proportional⇒APDQ = ABDEIn ∆CAP and ∆FDQ∠CAP = ∠FDQ  Using 1∠C = ∠F  Given⇒∆CAP~ ∆FDQ   AA

In the given figure ∆ A B C ~ ∆ D E F . AP bisects ∠ C A B and DQ bisects ∠ F D E . Prove that (a) A P D Q = A B D E (b) ∆ C A P ~ ∆ F D Q

In the given figure $∆ A B C ~ ∆ D E F$ . AP bisects $∠ C A B$ and DQ bisects $∠ F D E$ .

Prove that
(a) $\frac{A P}{D Q} = \frac{A B}{D E}$
(b) $∆ C A P ~ ∆ F D Q$