Drag the missing statements and reasons to the correct spot to complete the proof

The two column proof can be presented as follows;

1. ≅                     Given

2. ≅                    Given

3. ≅

4. ΔABD ≅ ΔBCD           SSS

Step-by-step explanation:

Given that we have;

Segment of triangle ΔABD being congruent to the corresponding segment of triangle ΔBCD and segment of triangle ΔABD being congruent to the corresponding segment of triangle ΔBCD, and that the common segment of both triangles are congruent by reflexive property, we have that ΔABD is congruent to ΔBCD by the Side-Side-Side (SSS) rule of congruency.

theres no picture: /

step-by-step explanation:

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for