Answer:
The Proof is given below.
Step-by-step explanation:
Given:
1.[tex]\overline{ZW}\ ||\ \overline{YX}[/tex]
2.[tex]\overline{ZW} \cong \overline{YX}[/tex]
To Prove:
Δ XYZ ≅ Δ ZWX
Proof:
[tex]\overline{ZW}\ ||\ \overline{YX}[/tex].........{given}
∴ ∠ WZX ≅ ∠YXZ ...{if lines are parallel then alternate angles are equal}..( 1 )
Now, In Δ XYZ and Δ ZWX
XY ≅ ZW ……….{Given}
∠ YXZ ≅ ∠ WZX ..……..{ Alternate Angles Property or From ( 1 )}
XZ ≅ ZX ……….{Reflexive Property}
∴ Δ XYZ ≅ Δ ZWX ….......{By Side-Angle-Side test}
..Proved
