Question

which sentence best explains why shape 1 and shape 2 are not congruent?
a. not all corresponding pairs of sides on the two shapes are parallel.
b. shape 1 cannot be mapped onto shape 2 using a reflection.
c. there is no sequence of rigid transformations that will map shape 1 onto shape 2.
d. shape 1 cannot be mapped onto shape 2 using a dilation.
e. not all corresponding pairs of sides on the two shapes are perpendicular.

Explanation:

Step1: Recall Congruence Definition

Congruent shapes can be mapped via rigid transformations (translation, rotation, reflection). Non - congruent means no such sequence exists.

Step2: Analyze Each Option

• Option A: Side parallelism isn't a congruence condition. Eliminate.
• Option B: Reflection is a rigid transformation, but the issue is not about reflection alone. Eliminate.
• Option C: Rigid transformations preserve size and shape. If no sequence of rigid transformations maps shape 1 to 2, they aren't congruent. This fits.
• Option D: Dilation changes size (for non - scale - factor 1), but congruence is about rigid transformations (no dilation). Eliminate.
• Option E: Side perpendicularity isn't a congruence condition. Eliminate.

Answer:

C. There is no sequence of rigid transformations that will map shape 1 onto shape 2.