The rule (x, y)→(2x,2y) maps △def to △d′e′f′. which statement correctly describes the relationship between △def and △d′e′f′ ? a. the triangles are congruent because △d′e′f′ is a rotation of △def , and a rotation is a rigid motion. b. the triangles are not congruent because △d′e′f′ is a dilation of △def , and a dilation is not a rigid motion. c. the triangles are not congruent because △d′e′f′ is a translation of △def , and a translation is not a rigid motion. d. the triangles are congruent because △d′e′f′ is a reflection of △def , and a reflection is a rigid motion.

B. The triangles are not congruent because △D′E′F′ is a dilation of △DEF , and a dilation is not a rigid motion.

Step-by-step explanation:

Given : The rule (x,y)→(2x,2y) maps △DEF to △D′E′F′.

We can see that a scale factor (2) is used in the above rule.

Rigid motions do not use any scale factor.

The transformation that uses scale factor to transforms figure is dilation.

And Dilation is not rigid motion because it does not produce congruent images.

Hence,  The triangles are not congruent because △D′E′F′ is a dilation of △DEF , and a dilation is not a rigid motion.

answer: (c) m∠qpo + (2x + 16)° = 180°

step-by-step explanation:

the opposite angles of a quadrilateral are supplementary.

so, ∠o + ∠q = 180°   and   ∠p + ∠r = 180°

since ∠r = 2x + 16°, we can use substitution as follows:

∠p + ∠r = 180°

∠p + (2x + 16)° = 180°