Question

3 triangle hef is the image of triangle fgh after a 180 - degree rotation around point k. select all statements that must be true. a triangle fgh is congruent to triangle feh. b triangle efh is congruent to triangle gfh. c angle khe is congruent to angle kfg. d angle ghk is congruent to angle khe. e segment eh is congruent to segment fg. f segment gh is congruent to segment ef.

Explanation:

Step1: Recall rotation properties

A rotation is a rigid - motion transformation. Rigid - motion transformations preserve side - lengths and angle - measures, which means the pre - image and the image are congruent. Triangle HEF is the image of triangle FGH after a 180° rotation around point K. Corresponding parts of congruent triangles are congruent.

Step2: Analyze option A

There is no indication that triangle FGH is congruent to triangle FEH. They are not related by the given rotation.

Step3: Analyze option B

Since triangle HEF is the image of triangle FGH after rotation, triangle EFH (same as triangle HEF) is congruent to triangle GFH.

Step4: Analyze option C

Corresponding angles in a rotation are congruent. Angle KHE and angle KFG are corresponding angles in the rotation of the triangles about point K, so they are congruent.

Step5: Analyze option D

There is no reason to believe that angle GHK is congruent to angle KHE. They are not corresponding angles in the rotation.

Step6: Analyze option E

Segment EH and segment FG are corresponding sides in the rotation of triangle FGH to triangle HEF, so segment EH is congruent to segment FG.

Step7: Analyze option F

Segment GH and segment EF are corresponding sides in the rotation of triangle FGH to triangle HEF, so segment GH is congruent to segment EF.

Answer:

B. Triangle EFH is congruent to triangle GFH.
C. Angle KHE is congruent to angle KFG.
E. Segment EH is congruent to segment FG.
F. Segment GH is congruent to segment EF.