Question

question 9
from the information in the diagram, can you prove \\( \triangle f d g \cong \triangle f d e \\)? explain.
no
yes, by aaa
yes, by asa
yes, by sas

Explanation:

Step1: Identify corresponding angles and side

In \(\triangle FDG\) and \(\triangle FDE\), \(\angle G=\angle E\) (given as marked angles), \(\angle DFG = \angle DFE\) (given as marked angles), and \(DF = DF\) (common side).

Step2: Apply ASA congruence criterion

The Angle - Side - Angle (ASA) congruence criterion states that if two angles and the included side of one triangle are equal to two angles and the included side of another triangle, then the two triangles are congruent. Here, in \(\triangle FDG\) and \(\triangle FDE\), we have two pairs of equal angles (\(\angle G=\angle E\) and \(\angle DFG=\angle DFE\)) and the included side \(DF\) common. So, \(\triangle FDG\cong\triangle FDE\) by ASA.

Answer:

yes, by ASA