Given that
In ∆ ABD , AB = BD------(1)
=> Angle B = Angle D
Since the angles opposite to equal sides are equal.
=> Angle A = Angle D
and
BC bisects Angle B
=> Angle BCA = Angle CDB ----(2)
And
BC = BC (Reflexive Property) -----(3)
From Eqⁿ(1),(2)&(3) we have
BA = BD
< ABC = BCD
BC = BC ( Common Side)
Therefore, ∆ ABC =~ ∆ DBC
by SAS property
Hence, proved.
Additional comment:
- The angles opposite to equal sides are equal.
- In two triangles , the two sides and the included angle of the first triangle are equal to the corresponding two sides and the included angle in the second triangle then they are congruent and this property is called Side-Angle-Side (SAS) Property.
- CPCT - Corresponding parts in the Congruent triangles are equal.
- Angle bisector divides the angle into two equal parts.
- The sum of two adajacent angles is 180° they are called Linear Pair.
also read similar questions:Given: AD perpendicullar DB, DB perpendicullar BC, AB = CD Prove: AB||DC..
https://brainly.com/question/20369276?referrer
given: AB ≈ DC ; AC ≈ DB PROVE: ABC ≈ DCB THE DIAGRAM SHOWS A 2 COLUM PROOF. ORDER THE REASONS SHOWN IN THE LIST TO MATCH THE STATEMENTS ......
https://brainly.com/question/22172471?referrer
