In the above bridge, line segment bd is the perpendicular bisector of line segment ac. for the bridge to be safe, triangle abd is congruent to triangle cbd. considering strictly the information that was given, what sequence of reasons can you use to prove that triangle abd is congruent to triangle cbd?

we can get the sequence of reasons with help of below explanation.

Step-by-step explanation:

Here It is given that, line segment BD is the perpendicular bisector of line segment AC. ( shown in below diagram)

By joining points B with A and B with C ( Construction)

We get two triangles ABD and CBD.

We have to prove that : Δ ABD ≅ Δ CBD

      Statement                                                  Reason

1. AD ≅ DC                                    1. By the property of segment bisector

2. ∠BDA ≅ ∠ BDC                        2. Right angles

3. BD ≅ BD                                   3. Reflexive

4.  Δ ABD ≅ Δ CBD                      4. By SAS postulate of congruence

he used the algebra tiles correctly.

step-by-step explanation:

given : 3x(2x-1)

solution :

since he used algebra tiles .

armando's solution is the same in the solution shown in figure

as he distributed 2x into x and x and wrote them vertically

and also write   -1 vertically

and 3x into x and x and x and wrote it horizontally

performing the multiplication in the algebra tiles we get

and solving the given expression :

3x(2x-1)

since solving the expression using tiles   and solving the expression algebraically we get the same answer

thus   we can choose the first statement as the answer to this problem which is "he used the algebra tiles correctly".