Questions: Identify the corresponding congruent angles and sides.

Identify the corresponding congruent angles and sides.
Transcript text: Identify the corresponding congruent angles and sides.
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Solution

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Solution Steps

To identify corresponding congruent angles and sides, we need to compare two geometric figures, typically triangles, and determine which angles and sides are equal in measure. This often involves using properties of congruent figures, such as the Side-Angle-Side (SAS) or Angle-Side-Angle (ASA) postulates. In Python, we can represent the figures as lists of angles and sides, and then compare these lists to find matches.

Step 1: Identify Congruent Angles

We compare the angles of both figures. The angles in both figure1 and figure2 are \(60^\circ\). Since all angles are equal, we find that the congruent angles are: \[ (60^\circ, 60^\circ) \] This congruence occurs for each pair of angles in the two figures, resulting in a total of 9 pairs of congruent angles.

Step 2: Identify Congruent Sides

Next, we compare the sides of both figures. The sides in both figure1 and figure2 are \(5\). Since all sides are equal, we find that the congruent sides are: \[ (5, 5) \] This congruence occurs for each pair of sides in the two figures, resulting in a total of 9 pairs of congruent sides.

Final Answer

The congruent angles are \(60^\circ\) and the congruent sides are \(5\). Thus, we can summarize the results as follows: \[ \text{Congruent Angles: } \boxed{(60^\circ, 60^\circ)} \] \[ \text{Congruent Sides: } \boxed{(5, 5)} \]

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