Question

In the diagram, AB=BC=CD=DA prove that triangle ADB is congruent to triangle CDB

Answer 1

For this problem you will want to use the SSS postulate which is the Side, Side, Side theorem. This means that if you prove three sides of two triangles congruent, then the triangle is congruent. You already know that two sides are congruent, so use the reflexive property and prove DB congruent to DB

Answer 2

Answer:

Since ,AB=BC=CD=DA the figure is a rhombus. This implies that opposite angles are congruent. In particular, we have angle A is congruent to angle C.So, triangle ADB and triangle CDB have two sides in common (AD=CD and AB=BC), and the angle between those side in common (angle A=angle C).So, by the SAS criterion, they are congruent. Also they are congruent since they have the same sides which follow the congruence of SSS