Question

explain 1 determining if figures are congruent
read explain 1 and complete your turn #1 - 2 (adapted from lesson 3.2) and complete the following.
a way to determine if two geometric figures are congruent is to show that one figure maps onto the other by a sequence of rigid motions, such as a sequence of reflections, translations, and or rotations. this was practiced in lesson 3.1 sequences of transformations. first, practice with just one transformation.
example
the figures shown are congruent. find a rigid motion that maps one figure to the other. give coordinate - notation for the transformations you use.
① cdef≅jklm
part 1: figure cdef can be mapped onto jklm by...
□ a rotation
□ b reflection
□ c translation
□ d the figures are not congruent.
the answer is b
part 2: the coordinate notation is (x,y)→( - x,y); a reflection across the y - axis
② △abc≅△xyz
part 1: figure abc can be mapped onto xyz by...
□ a rotation
□ b reflection
□ c translation
□ d the figures are not congruent.
the answer is a
part 2: the coordinate notation is (x,y)→( - y,x); a rotation of 90°

Explanation:

Step1: Analyze CDEF and JLMK

By observing the orientation of CDEF and JLMK, we see a mirror - like relationship.

Step2: Identify transformation type

A reflection across the y - axis can map CDEF onto JLMK. The coordinate notation for reflection across the y - axis is $(x,y)\to(-x,y)$.

Step3: Analyze ABC and XYZ

By observing the orientation of ABC and XYZ, we note a 90 - degree turn relationship.

Step4: Identify transformation type

A 90 - degree rotation can map ABC onto XYZ. The coordinate notation for a 90 - degree rotation is $(x,y)\to(-y,x)$.

Answer:

For CDEF and JLMK:

1. B. Reflection
2. $(x,y)\to(-x,y)$; a reflection across the y - axis

For ABC and XYZ:

1. A. Rotation
2. $(x,y)\to(-y,x)$; a rotation of 90°