Question

2.12.2 from conjecture to proof
draw an auxiliary line from point e to point g to make two
triangles.
name the triangles below.
i divided the rectangle into (\triangle) fhe and (\triangle) hfg.
draw in all of the congruency marks you know:

• (ef = gh) (given)
• (fg = he) (given)
• (eg = ge) (?)

what rule tells us that eg is congruent to itself?
i will use de to say that eg is congruent to itself.

Explanation:

Step1: Name the triangles

When we draw a line from \(E\) to \(G\), the two triangles formed are \(\triangle EHG\) and \(\triangle FGE\).

Step2: Congruence of \(EG\) to itself

The reflexive property of congruence states that any segment (or angle, or geometric figure) is congruent to itself. For segment \(EG\), by the reflexive property of congruence, \(EG\cong GE\)

Answer:

I divided the rectangle into \(\triangle EHG\) and \(\triangle FGE\). I will use the reflexive property of congruence to say that \(EG\) is congruent to itself.