Question

example 4 determine congruence. is the pair of objects congruent? if the pair of objects is congruent, describe a composition of rigid motions that maps one to the other. example 3 identify congruent figures. explain how you know whether or not the following figures are congruent. explain: explain: explain: so, two figures are congruent if all corresponding and are congruent. label the sides and angles of the figures so that the two quadrilaterals are congruent.

Explanation:

Step1: Recall congruence definition

Two figures are congruent if all corresponding sides and angles are equal. Rigid - motions (translations, rotations, reflections) preserve congruence.

Step2: Analyze first pair (puzzle - pieces)

The two puzzle - pieces have the same shape and size. A translation (sliding) can map one to the other. So, they are congruent.

Step3: Analyze second pair (3 - D shapes)

The two 3 - D shapes do not have the same shape. The depth and orientation are different. So, they are not congruent.

Step4: Analyze grid - based figure

Check side lengths and angles. If all corresponding sides and angles are equal, the figure is congruent. Can use distance formula for side - lengths and angle - measurement tools for angles.

Step5: Analyze triangle pairs

For the first two triangles, if two angles and the included side (ASA - Angle - Side - Angle) are equal, they are congruent. For the third triangle, compare its sides and angles with the others.

Answer:

• Puzzle - pieces: Yes, translation
• 3 - D shapes: No
• Grid - based figure: Analyze side lengths and angles
• First two triangles: Likely congruent if ASA holds
• Third triangle: Compare with others to determine congruence