Question

Let angle C be congruent to angle C' and POC be congruent to P'O'C'.Let O" be a point on line CO so that CO" is equal to C'O'. Let P" be the point on line CP so that the dilation of P is represented by P".Which statement is true?A. triangle COP is equal to triangle C'O'P'B. line CP is congruent to line CP"C. triangle C'O'P is a glide reflection of triangle COP, whereas triangle CO"P" is congruent to triangle C'O'P'D. triangle CO"P" is a dilation of triangle COP with center C and a scale factor of r = C'O'/CO equals CO/CO

Answer 1

ANSWER

D. Triangle CO''P'' is a dilation of triangle COP with center C and a scale factor of r = C'O'/CO = CO''/CO

EXPLANATION

Given:

• ∠C ≅ ∠C'

,

• ∠POC ≅ ∠P'O'C'

,

• C'O' = CO''

Triangles COP and C'O'P' are similar triangles, by AA postulate.

Since CO'' and C'O' have the same length - they are congruent, then angle CO''P'' is congruent to angle C'O'P', and we can conclude that segments O''P'' and OP are parallel:

Hence, triangle CO''P'' is a dilation of triangle COP with center C and a scale factor of r = C'O'/CO = CO''/CO