Question

overlapping triangles
which of the following
asa
sss
sas
hl
\\(\angle aeb \cong \angle cdb\\)
\\(\overline{eb} \cong \overline{db}\\)

Explanation:

Identify given geometric information

Using the Triangle Congruence Postulates knowledge point, we analyze the given congruent parts:

• Angle: \(\angle AEB \cong \angle CDB\)
• Side: \(\overline{EB} \cong \overline{DB}\)

Find additional congruent parts

Using the Vertical Angles knowledge point, we identify the vertical angles formed by intersecting lines \(\overline{AD}\) and \(\overline{CE}\):

• \(\angle ABE \cong \angle CBD\)

Determine the congruence postulate

Using the ASA Congruence knowledge point, we compare the parts of \(\triangle ABE\) and \(\triangle CBD\):

• Angle: \(\angle AEB \cong \angle CDB\)
• Included Side: \(\overline{EB} \cong \overline{DB}\)
• Angle: \(\angle ABE \cong \angle CBD\)

Since two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, the triangles are congruent by ASA.

Answer:

• ASA (Correct answer)
• SSS
• SAS
• HL