answer: the paragraph proof is mentioned below.
step-by-step explanation:
given: in a δxwy where
such that, ∠wzx ≅ ∠yzx and zw≅zy
we have to prove that: segment zx is a perpendicular bisector of segment wy.
prove: since, zw≅zy ⇒ ∠wzy is a supplementary angle.
then, ∠wzy= 180°
⇒∠wzx + ∠yzx = 180° ( because xz divides ∠wzy into two parts)
but, ∠wzx ≅ ∠yzx ( given)
⇒∠wzy+∠wzy=180° ( by substitution)
⇒2∠wzy=180°
⇒∠wzy=90°
⇒∠wzy=∠yzx =90°
therefore, xz⊥wy where wz=zy
⇒zx is a perpendicular bisector of wy.