Questions: What can we prove to be true using the reflexive property for this diagram?
angle DAE congruent to angle BAC
AE congruent to AD
angle ADE congruent to angle AED
angle CBA congruent to angle BCA
Transcript text: What can we prove to be true using the reflexive property for this diagram?
$\angle D A E \cong \angle B A C$
$A E \cong A D$
$\angle A D E \cong \angle A E D$
$\angle C B A \cong \angle B C A$
Solution
Step 1: Understanding the Reflexive Property
The reflexive property states that any geometric figure is congruent to itself. In terms of angles, it means any angle is congruent to itself. In terms of line segments, any line segment is congruent to itself.
Step 2: Applying the Reflexive Property to the Diagram
We are looking for an angle or a side that is shared by two triangles or that is part of the same triangle in the provided diagram. The shared side between triangles $\triangle ABC$ and $\triangle ACB$ is $\overline{BA}$ (which is the same as $\overline{AB}$). By the reflexive property, this shared side must be congruent to itself.
Step 3: Final Answer
$\overline{AB} \cong \overline{AB}$ (Alternatively written as $\overline{BA} \cong \overline{BA}$)