A series of rigid motions maps ΔUVW onto ΔRST. Based on this information, which of the following is a true statement? Question 12 options: A) ΔUVW is half the area of ΔRST. B) The corresponding pairs of angles of ΔUVW and ΔRST are congruent, but the corresponding sides aren't. C) ΔUVW and ΔRST are congruent. D) There isn't enough information to make a statement about ΔUVW and ΔRST.

 C) ΔUVW and ΔRST are congruent

Step-by-step explanation:

There are four kinds of rigid transformation.

1) translation 2) reflection 3) rotation 4) glide reflection.

If a series of rigid motions maps ΔUVW onto ΔRST.

Then, ΔUVW and ΔRST must be congruent. (No change in size or shape)

hence, the correct statement is C) ΔUVW and ΔRST are congruent.

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step-by-step explanation:

1. 180°. the sum of the interior angles of a triangle is 180°, for the equilateral triangle that it has three equals side is 60°+60°+60°=180°.

2. 60°. each interior angle of a equilateral triangle is 60°

3. 120°. the measure of ∠m is 120°, the sum of the angles ∠m and ∠n is equal to 180°. so, in order to find the measure of ∠m, we have ∠m+∠n=180° > ∠m=180°-∠n > ∠m=180°-60°=120°.

4. 360°. the sum of the exterior angles of an equilateral triangle is ∠m+∠r+∠x=120°+120°+120°=360°. the exterior angles of any triangle always add 360°.