∠TEB=∠ETS

∠BTE=∠SET

BE=ST

Both 1 and 2 are correct

$\angle APB\cong\angle CPD$ ; Vertical Angles

$\angle A\approx\angle D$ ; Alternate Interior Angles

$\angle C\cong\angle B$ ; Alternate Interior Angles

$\overline{AB}\cong\overline{CD}$ ; Prove

Vertical Angles are Congruent, SAS(Side-Angle-Side)

Reflexive Property, SAS(Side-Angle-Side)

Definition of a Midpoint, SSS(Side-Side-Side)

Reflexive Property, SSS(Side-Side-Side)

T is the midpoint of segment BG and

∠B≅∠G

∠B≅∠G and ∠A≅∠W

T is the midpoint of segment BG and ∠A≅∠W

T is the midpoint of segment AW and ∠A≅∠W

$\overline{DC}\cong\overline{DC}$ ; Reflexive Property

$\angle A\cong\angle B$ ; Reflexive Property

$\angle1\cong\angle2$ ; Reflexive Property

$\overline{AD}\cong\overline{DB}$ ; Definition of a Midpoint

IA=AE

∠IAD = ∠DAE

∠IDA=∠EDA

∠IAD and ∠DAE are right angles

Reflexive Property

Definition of Midpoint

Given

Vertical Angles Theorem