Question

The figure below shows a quadrilateral ABCD with diagonal BD bisecting angle ADC:

A quadrilateral ABCD is drawn with BD as a diagonal. BD bisects angle ADC and forms two triangles ABD and CBD. AB and CB are equal in length. (I attached a picture to the question).

Which equation is true?
A) DB = 2DC
B) AD = DC
C) AB = DB
D) AB = 2AD

Answer 1

The answer would be B) AD=DC, the reason why is because line AD is a reflection of line DC

Answer 2

Answer with explanation:

In Quadrilateral A B CD

Diagonal BD bisects angle D.

→→ ∠A DB=∠ C DB

In ΔA DB and ΔC DB

1. AB= CB→→→→[Given]

2. ∠A DB=∠ C DB-------[Given]

3. BD=BD ----[Common side]

⇒ ΔA DB ≅ ΔC DB→→→[S A S]

AD=DC→→→→[C P C T]

Option B:⇒ AD = DC