Triangles \(ABC\) and \(DCB\) are congruent, as shown below, where \(AB \neq AC.\)

https://latex.artofproblemsolving.com/c/e/0/ce0bd0c8c119e8879323319f2bd1f3d606500f59.png   <-----link to the image (sorry if it's super dark)

(a) Show that triangles \(ABD\) and \(DCA\) are congruent.

(b) Show that \(\angle ADB = \angle DBC.\)

 Dec 20, 2019

(a)  Assuming  that  we have an isosceles trapezoid


AB  = DC               sides of an isoceles trapezoid are equal


Angle ABC  = Angle DCB      base angles of an isoceles trapezoid are equal


Angle ABC + Angle DAB  = 180          opposite angles in an isoceles trapezoid are  supplementary

Angle  DCB  + Angle ADC  = 180


Angle DAB  = Ange  ADC                subtraction property of equality


AD  = AD                                       reflexive property       


Triangle  ABD  is congruent to Triangle DCA         By   SAS




AD  is parallel to BC            bases of anisoscees trapezoid are  parallel


Angle ADB  = Angle DBC         a transversal  cutting parallel lines   makes alternate interior angles equal



 cool cool cool

 Dec 20, 2019

12 Online Users