Question

rag each description into the correct category. nswer choices: drag the answer choices to the correct category over here! one figure has been rotated 180° but sides and angles still match same area, different side lengths one is reflected and translated but still matches exactly identical shapes but different sizes same side lengths and same angle measures

Explanation:

• Congruent Figures:
• Rotation of \(180^{\circ}\) with sides and angles matching: Rotation is a rigid transformation. If after a \(180^{\circ}\) rotation, sides and angles match, the figures are congruent.
• Reflection and translation with exact match: Reflection and translation are also rigid transformations. If after these transformations the figures match exactly, they are congruent.
• Same side lengths and same angle measures: By the definition of congruent figures (SSS - Side - Side - Side, SAS - Side - Angle - Side etc. congruence criteria in geometry), if side lengths and angle measures are the same, the figures are congruent.
• Not Congruent Figures:
• Same area, different side lengths: Area is a measure of space enclosed. Two non - congruent figures (e.g., a rectangle with length \(l = 4\), width \(w = 3\) and a parallelogram with base \(b=6\), height \(h = 2\)) can have the same area (\(A = 12\)) but different side lengths.
• Identical shapes but different sizes: If shapes are of different sizes (even if they are similar in shape, like two circles with different radii or two squares with different side lengths), they are not congruent. Congruent figures must be of the same size.

Answer:

• Congruent Figures:
• One figure has been rotated \(180^{\circ}\) but sides and angles still match.
• One is reflected and translated but still matches exactly.
• Same side lengths and same angle measures.
• Not Congruent Figures:
• Same area, different side lengths.
• Identical shapes but different sizes.