23. Identify the congruence criteria for triangles ADE and BDE based on the markings. Provide a step-by-step explanation.

Step-by-step explanation:

• Step 1: Analyze the markings. In triangle ADE and triangle BDE, we see that AD is marked with a single dash and BD is marked with a single dash, indicating AD = BD. DE is common to both triangles, so DE = DE. Angle ADE is marked with a single arc and angle BDE is marked with a single arc, indicating $$\angle ADE = \angle BDE$$.
• Step 2: Identify the congruence criterion. We have two sides and an angle. AD = BD (Side), DE = DE (Side), and $$\angle ADE = \angle BDE$$ (Angle). The angle $$\angle ADE$$ is included between sides AD and DE. The angle $$\angle BDE$$ is included between sides BD and DE.
• Step 3: Apply the SAS congruence criterion. Since two sides and the included angle of triangle ADE are equal to the corresponding two sides and the included angle of triangle BDE (AD=BD, $$\angle ADE = \angle BDE$$, DE=DE), the triangles are congruent by the Side-Angle-Side (SAS) congruence postulate.

Answer: Triangles ADE and BDE are congruent by the SAS (Side-Angle-Side) congruence criterion.