Question

1. the quadrilateral math was rotated 90 degrees counterclockwise followed by a translation to produce the quadrilateral math. click in the table below to show which side lengths are equal to the lengths of the given line segments. line segment ma a b c d line segment at line segment th line segment hm

Explanation:

Step1: Recall Transformations Properties

Rotations and translations are rigid transformations. Rigid transformations preserve the length of line segments. So, after a 90° counterclockwise rotation and a translation, the length of each side of quadrilateral MATH will be equal to the length of the corresponding side of quadrilateral M'A'T'H'.

Step2: Match Corresponding Segments

• For line segment MA: Find the corresponding segment in M'A'T'H' (which is M'A') and match it to the equal - length segment in the red quadrilateral.
• For line segment AT: The corresponding segment is A'T', so find the equal - length segment in the red quadrilateral.
• For line segment TH: The corresponding segment is T'H', so find the equal - length segment in the red quadrilateral.
• For line segment HM: The corresponding segment is H'M', so find the equal - length segment in the red quadrilateral.

Assuming the red quadrilateral has sides a, b, c, d:

• Line segment MA should be equal in length to the side of the red quadrilateral that corresponds to M'A' (let's say if MA corresponds to side c, then we mark c for MA).
• Line segment AT should be equal in length to the side corresponding to A'T' (say side d, mark d for AT).
• Line segment TH should be equal in length to the side corresponding to T'H' (say side a, mark a for TH).
• Line segment HM should be equal in length to the side corresponding to H'M' (say side b, mark b for HM).

(Note: The actual matching depends on the precise coordinates of the vertices, but the key is using the property of rigid transformations preserving length.)

Answer:

The table should be filled as follows (assuming the above - mentioned correspondences, actual values depend on vertex coordinates):

Line segment MA	c
Line segment TH	a
Line segment HM	b

(The specific letters may vary based on the exact length matching from the graphs, but the principle is rigid transformations preserve side lengths.)