The irregular figure on the left has been decomposed into the figures on the right.

A figure is broken into a parallelogram and rectangle. The rectangle has a base of 7 centimeters and a height of 4 centimeters. The parallelogram has a base of 7 centimeters and a height of 5 centimeters.
What is the value of w, the width of the parallelogram?
4 centimeters
5 centimeters
7 centimeters
9 centimeters

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.

Which statement accurately explains whether a reflection over the y axis and a 270° counterclockwise rotation would map figure acb onto itself?

Which of the following would be a correct step in proving that triangle abc is congruent to triangle cda? a. use a protractor to measure the angles and show that all the corresponding angles are equal in measure. this will allow you to prove congruence by aaa. b. show that segment ab is parallel to segment cd and segment ad is parallel to segment cb. this will allow you to prove congruency by asa. c. show that is segment ab is perpendicular to segment ad. this will allow you to prove congruence by sas. d. none of the above.