Question

I don’t know how to do a flow chart at all pls help

Answer 1

Given:

AB || DE

BC = 14

CD = 7

CE = 7

DE = 5

To prove:

The two triangles are congruent.

Consider the two triangles ABC and EDC.

`\begin{gathered} \angle BCA=\angle\text{DCE ( Vertical angles)} \\ \angle ABC=\angle EDC\text{ (Alternate angles)} \\ \angle BAC=\angle DEC\text{ (Alternate angles)} \end{gathered}`

By AAA similarity, If any two angles of a triangle are equal to any two angles of another triangle, then the two triangles are similar to each other.

Therefore,

`\Delta ABC\approx\Delta EDC`

So, the corresponding sides are proportional.

`\begin{gathered} (AB)/(ED)=(BC)/(DC)=(AC)/(EC) \\ (AB)/(5)=(14)/(2)=(AC)/(7) \\ (AB)/(5)=7=(AC)/(7) \end{gathered}`

So, equating (1) and (2), we get

AB = 35

So, equating (2) and (3), we get

AC = 49

Thus, the missing sides are AB=35 and AC=49.