A sequence of transformations is described below.
- A reflection over a line $\overleftrightarrow{P Q}$
- A rotation about the point $P$
- Another reflection over $\overleftrightarrow{P Q}$
- A rotation about the point $Q$

Which of the following must be preserved under this sequence of transformations?

Choose 1 answer:
(A) Angle measures only
(B) Segment lengths only
(C) Both angle measures and segment lengths
(D) Neither angle measures nor segment lengths

Question

A sequence of transformations is described below.
- A reflection over a line $\overleftrightarrow{P Q}$
- A rotation about the point $P$
- Another reflection over $\overleftrightarrow{P Q}$
- A rotation about the point $Q$

Which of the following must be preserved under this sequence of transformations?

Choose 1 answer:
(A) Angle measures only
(B) Segment lengths only
(C) Both angle measures and segment lengths
(D) Neither angle measures nor segment lengths

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ A reflection over a line $ \overleftrightarrow{PQ} $ preserves both angle measures and segment lengths. ‖ ‖ step 2 ⋮ A rotation about a point $ P $ also preserves both angle measures and segment lengths. ‖ ‖ step 3 ⋮ Another reflection over $ \overleftrightarrow{PQ} $ again preserves both angle measures and segment lengths. ‖ ‖ step 4 ⋮ A rotation about a point $ Q $ preserves both angle measures and segment lengths. ‖ ‖ step 5 ⋮ Since all transformations in the sequence preserve both angle measures and segment lengths, the overall sequence must preserve both angle measures and segment lengths. ‖ ***C*** ∻Key Concept∻ ⚹Preservation of geometric properties under transformations⚹ ∻Explanation∻ ⚹Reflections and rotations are rigid motions that preserve both angle measures and segment lengths.⚹◊What is the relationship between the angle measures and segment lengths in transformations involving reflections and rotations⍭ Generate me a similar question◊

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