Question

19 given: dg = eg, gh = gf name the postulate or theorem you can use to prove △dgf ≅ △egh. aas theorem asa postulate sas postulate sss postulate

Explanation:

Step1: Identify given side - equalities

We are given that $\overline{DG}=\overline{EG}$ and $\overline{GH}=\overline{GF}$.

Step2: Identify the included angle

$\angle DGF$ and $\angle EGH$ are vertical angles, so $\angle DGF=\angle EGH$.

Step3: Recall triangle - congruence postulates

The Side - Angle - Side (SAS) postulate states that if two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the two triangles are congruent. Here, in $\triangle DGF$ and $\triangle EGH$, we have two pairs of equal sides ($DG = EG$ and $GH = GF$) and the included equal angles ($\angle DGF=\angle EGH$).

Answer:

SAS Postulate