Segment GH underwent a sequence of two rotations around the same center. The original length of GH¯¯¯¯¯¯¯¯ is 7 meters. What is the length of the segment after the sequence of rotations?

Abby is preparing fruit punch for her party. she starts with a bowl filled with liquid that has 1/2 fruit juice and 1/2 sprite, but she decides it's too fruity. so she pours out 1/4 of the liquid, and then fills the bowl up again with sprite. what fraction of the punch is now sprite?

Read the equations in the table below. then drag a description of the situation and a table to represent each equation. indicate whether each of the relationships is proportional or non-proportional.

In the figure below, ∠dec ≅ ∠dce, ∠b ≅ ∠f, and segment df is congruent to segment bd. point c is the point of intersection between segment ag and segment bd, while point e is the point of intersection between segment ag and segment df. the figure shows a polygon comprised of three triangles, abc, dec, and gfe. prove δabc ≅ δgfe.