Question

Help appreciated!!!

Consider a dilation of polygon ABCDEF from center O with scale factor r resulting in its image, polygon A'B'C'D'E'F'.

If EDC measures 117° then the measure of E'D'C' is___ If AB measures 1.8 inches and A'B' measures 4.5 inches, then the scale factor r is____

Name one segment from polygon ABCDEF and one segment from polygon A'B'C'D'E'F' that are parallel.​

Answer 1

Explanation:

in a dilation all the angles stay the same. only the lengths of lines (like sides or heights) change - and all with the same scale factor (which makes the original and the dilated result similar objects).

angle EDC = 117°.

therefore angle E'D'C' = 117°.

AB = 1.8 in

A'B' = 4.5 in

the scale factor r is

r = 4.5 / 1.8 = 2.5

every segment of A'B'C'D'E'F' is parallel to its original counterpart in ABCDEF.

like

AB to A'B'

as well as

BC to B'C'

CD to C'D'

DE to D'E'

EF to E'F'

that is the reason why projections work (even at an inclined angle of the projection screen the picture might seem strangely stretched, but the angles are still all the same, parallel lines remain parallel, perpendicular lines remain perpendicular, ... - and the viewer still recognizes the pictures).