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7. Quadrilateral MATH is congruent to quadrilateral WXYZ. Which statement is always true?



(1) Quadrilateral MATH and quadrilateral WXYZ are the same shape, but not necessarily the same size

(2) MA ≈XY

(3) m
(4) TH≈YZ

7 Quadrilateral MATH is congruent to quadrilateral WXYZ Which statement is always true 1 Quadrilateral MATH and quadrilateral WXYZ are the same shape but not

Answer :

Final answer:

When quadrilateral MATH is congruent to quadrilateral WXYZ, statement (4) TH≃YZ is always true because corresponding sides in congruent figures are equal, making TH equal to YZ in measurement. Therefore, the correct option is 4.

Explanation:

The question asks which statement is always true if quadrilateral MATH is congruent to quadrilateral WXYZ. Given congruency, every corresponding side pair and angle pair are equal in measure.

We consider each vertex of one polygon in correspondence with a vertex of the other polygon, in the order they are named. Therefore, if MATH is congruent to WXYZ, then side MA matches with side WZ, side AT matches with side ZX, side TH matches with side XY, and side HM matches with side YW.

Based on these correspondences, statement (2) MA ≃ XY is incorrect because MA should correspond to WZ. Statement (3) is incomplete.

Statement (4) TH≃YZ is the correct answer as side TH in MATH corresponds to side YZ in WXYZ when the polygons are congruent.

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