Question

from unit 2, lesson 2 triangle hef is the image of triangle hgf after a reflection across line fh. 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 hfe is congruent to angle fhg. d angle efg is congruent to angle ehg. e segment eh is congruent to segment fg. f segment gh is congruent to segment eh.

Explanation:

Step1: Recall reflection property

A reflection is a rigid - motion. Rigid - motions preserve congruence of figures, angles, and segments. When $\triangle HGF$ is reflected across line $FH$ to get $\triangle HEF$, corresponding parts of the pre - image and image are congruent.

Step2: Analyze triangle congruence

Since $\triangle HGF$ is reflected to $\triangle HEF$, $\triangle EHF\cong\triangle GHF$ (corresponding parts of congruent triangles). So, option B is correct.

Step3: Analyze angle congruence

Corresponding angles of congruent triangles are congruent. $\angle HFE$ and $\angle FHG$ are corresponding angles in the reflection, so $\angle HFE\cong\angle FHG$. Option C is correct.

Step4: Analyze segment congruence

Corresponding segments of congruent triangles are congruent. Segment $GH$ and segment $EH$ are corresponding segments in the reflection, so $GH\cong EH$. Option F is correct.

Answer:

B. Triangle $EFH$ is congruent to triangle $GFH$.
C. Angle $HFE$ is congruent to angle $FHG$.
F. Segment $GH$ is congruent to segment $EH$.