Question

geometry sem a geometry
congruence: sss and hl
the triangles shown are congruent by the sss congruence theorem.
the diagram shows the sequence of three rigid transformations used to map
△abc onto △abc. what is the sequence of the transformations?
translation, then reflection, then rotation
translation, then rotation, then reflection
rotation, then translation, then reflection
rotation, then reflection, then translation

Explanation:

Step1: Analyze translation

Translation is moving a figure without rotation or reflection. First, \(\triangle ABC\) is translated to get a new position (similar to \(\triangle A'B'C'\) in orientation before rotation and reflection).

Step2: Analyze rotation

Rotation is turning a figure around a point. After translation, the figure is rotated (to adjust the angle before reflection).

Step3: Analyze reflection

Reflection is flipping a figure over a line. After rotation, the figure is reflected (to match the final position of \(\triangle A''B''C''\)).

Answer:

translation, then rotation, then reflection