If a number is increased by 6 and the result is divided by 2, the number 5 is obtained. find the original number?

Call the original number x for now... x is increased by 6 so you have (x + 6)..
this is halved the get you 1/2x + 3 = 5. You subtract 3 from both sides and get 1/2 x = 2. Then multiply both sides by 2 and you get x = 4.

c.) Triangles ABD and CBD are congruent by the SAS Congruence Postulate.

Step-by-step explanation:

Line segment DB divides <ADC into two congruent angles. That is:

<ADB is congruent to <CDB

Segment DB of ∆ABD is congruent to segment DB of ∆CBD.

Also, Segment AD of ∆ABD is congruent to segment CD of ∆CBD.

This means two sides (DB and AD) and an included angle (<ADB) of ∆ABD are congruent to the corresponding two sides (DB and CD) and included angle (<CDB) of ∆CBD.

Therefore, by the SAS Congruence Postulate, ∆ABD is congruent to ∆CBD.