Prove the Composition Theorem by ordering the statements of the paragraph proof. Given Figure A is transformed to figure A' by a

Question

Prove the Composition Theorem by ordering the statements of the paragraph proof.
Given Figure A is transformed to figure A' by a rigid motion.
Figure A' is transformed to figure A' by a rigid motion.
Prove The composition of transformations from figure A to figure A" is a rigid motion.
= every part of figure A' is congruent to the corresponding part of figure A" by the definition of rigid motion.
= So, by the Transitive Property of Congruence, every part of figure A is congruent to the corresponding part of figure A".
= Given that figure A' is transformed to figure A" by a rigid motion,
= Given that figure A is transformed to figure A' by a rigid motion,
= every part of figure A is congruent to the corresponding part of figure A' by the definition of rigid motion.
= So, by the definition of rigid motion, the composition of rigid motions from figure A to figure A" is a rigid motion.

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