Question

determining if triangles are congruent
in △cde, m∠c = 30° and m∠e = 50°. in △fgh, m∠g = 100° and m∠h = 50°. are the triangles congruent? if so, write a congruency statement.
no, the triangles are not necessarily congruent.
yes, △cde ≅ △hgf
yes, △cde ≅ △fgh
yes, △cde ≅ △ghf

Explanation:

Step1: Find the measure of the third angle in \(\triangle CDE\)

The sum of angles in a triangle is \(180^{\circ}\). So, \(m\angle D=180^{\circ}-(m\angle C + m\angle E)=180^{\circ}-(30^{\circ}+ 50^{\circ}) = 100^{\circ}\)

Step2: Match the angles of the two triangles

In \(\triangle CDE\), the angles are \(30^{\circ},50^{\circ},100^{\circ}\). In \(\triangle FGH\), the angles are \(m\angle F=180^{\circ}-(m\angle G + m\angle H)=180^{\circ}-(100^{\circ}+50^{\circ}) = 30^{\circ}\), \(m\angle G = 100^{\circ}\), \(m\angle H=50^{\circ}\). But congruent triangles require corresponding sides to be equal as well. We only know the angles. Knowing that three angles are equal (AAA - Angle - Angle - Angle) is not a congruence criterion (it is a similarity criterion).

Answer:

No, the triangles are not necessarily congruent.