**1. <AEP is congruent
to <IEC **-*Vertical
<s are congruent*

**2. <APE is congruent
to <CIE ***- When two
parallel lines are cut by a transversal, alternate interior ,s
are congruent.*

**3. Triangle APE is
similar to triangle CIE ***-
Angle Angle similarity postulate*

**4. EA/EC=AP/CI ***- Corresponding sides of similar triangles
are proportionate*

**5. <BFH is congruent
to <AFP ***- Vertical
<s are congruent*

*6. <FHB is congruent
to <FPA **-When
two parallel lines are cut by a transversal, alternate interior
,s are congruent.*

**7. Triangle BFH is
similar to triangle AFP***-
Angle Angle similarity postulate*

**8. BF/AF=BH/AP***- Corresponding sides of similar triangles
are proportionate*

**9. <BPD is congruent
to <BIC ***-
When*** ***two
parallel lines are cut by a transversal, Corresponding angles
are congruent.*

**10. <PBD is congruent
to <IBC ***-
Reflexive property*

**11. Triangle BDP is
similar to triangle BCI***-
Angle Angle similarity postulate*

**12. DB/CB=PD/CI***- Corresponding sides of similar triangles
are proportionate*

**13. <PCD is congruent
to <HCB ***-*** ***Reflexive
property*

**14. <CPD is congruent
to <CHB ***-
When*** ***two
parallel lines are cut by a transversal, Corresponding angles
are congruent.*

**15. Triangle PCD is
similar to triangle HCB***-
Angle Angle similarity postulate*

**16. PD/HB=CD/BC*** -Corresponding sides of similar triangles
are proportionate*

**17. (PD)(BC)=(HB)(CD)
***- Cross multiplication
from line 16*

**18. (DB)(CI)=(BC)(PD)
***- Cross multiplication
from line 12*

**19. BH=((AP)(BF))/(AF)
***- Multiplication and
division from line 8*

**20. CI = ((AP)(EC))/(AE)
***- Multiplication and
division from line 4*

**21. (PD)(BC)= ((AP)(BF)(CD))
/ (AF)*** - Substitution
lines 17 and 19*

**22. ((DB)(AP)(EC))
/ (AE) = (PD)(BC) ***substitution
lines 18 and 20*

**23. ((AP)(BF)(CD))
/ (AF) = ((DB)(AP)(EC)) / (AE) ***Reflexive-lns
21 & 22*

**24. (AE)(AP)(BF)(CD)
= (AF)(DB)(AP)(EC)*** -
Multiply both sides by (AF)(AE)*

**25. (AE)(BF)(CD)=(AF)(DB)(EC)
***-Divide both sides by
(AP)*