Question

Han wrote a proof that triangle BCD is congruent to triangle DAB. Han's proof is incomplete. How can Han fix his proof?
DC∥AB
Line DC is parallel to and above line AB and cut by transversal DB. Angles A and C are right angles.
Line AB is parallel to line DC and cut by transversal DB. So angles CDB and ABD are alternate interior angles and must be congruent.
Side DB is congruent to side BD because they're the same segment.
Angle A is congruent to angle C because they're both right angles.
By the Angle-Side-Angle Triangle Congruence Theorem, triangle BCD is congruent to triangle DAB .

Answer 1

Answer:

sorry i didn't found the question

Answer 2

Han can fix his proof in the following way:

• Han's using Angle Side Angle property to prove that triangle BCD is congruent to triangle DAB.
• But his arguments that ∠A = ∠C), ∠ABD, = ∠BDC and sides BD = DB follow Angle Angle Side order (AAS). This congruency criterion is not valid. (Refer to the image attached below)
• Since the two triangles are right-angled triangles and two angles have been proven equal.

      ⇒∠ADB = ∠CBD  (Using the angle sum property of a triangle we can conclude that the third angle from both the triangle is also equal)

• Hence, using ASA congruency, Han can prove that both the triangles are congruent.