Question

1. which transformations preserve congruence and side lengths?

a. translation, reflections, dilations
b. translations, rotations, dilations
c. reflections, dilations, rotations
d. rotations, translations, reflections

1. given \\( \triangle z b w \cong \triangle x a y \\) what information can be correctly determined? select all that apply:

a. \\( z b \cong x a \\)
b. \\( w z \cong y a \\)
c. \\( b w \cong a y \\)
d. \\( \angle w b z \cong \angle x a y \\)

Explanation:

• For the first question:
• Translation: It is a rigid transformation that slides a figure without changing its shape, size, or orientation. So, it preserves congruence and side - lengths.
• Reflection: It is a rigid transformation that flips a figure over a line. It also preserves congruence and side - lengths.
• Rotation: It is a rigid transformation that turns a figure around a point. It preserves congruence and side - lengths.
• Dilation: It is a non - rigid transformation that changes the size of a figure (either enlarging or reducing). So, it does not preserve side - lengths.
• For the second question:
• If \(\triangle ZBW\cong\triangle XAY\), then by the property of congruent triangles (corresponding parts of congruent triangles are congruent - CPCTC):
• Corresponding sides: \(ZB\cong XA\) (side \(ZB\) in \(\triangle ZBW\) corresponds to side \(XA\) in \(\triangle XAY\)), \(BW\cong AY\) (side \(BW\) in \(\triangle ZBW\) corresponds to side \(AY\) in \(\triangle XAY\)), \(WZ\cong YX\) (not \(WZ\cong YA\)).
• Corresponding angles: \(\angle WBZ\cong\angle XAY\) (not \(\angle WSZ\cong\angle XAY\)).

Answer:

• For the first question: D. Rotations, Translations, Reflections
• For the second question: A. \(ZB\cong XA\); C. \(BW\cong AY\)