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Triangle FGH is the image of isosceles triangle FE~=HE FEH after a reflection across line HF. Select all the statements that are a result of corresponding parts of congruent triangles being congruent.

Triangle FGH is congruent to triangle FEH due to reflection, thus allowing us to conclude that all corresponding angles and sides are congruent. This leads to several statements regarding the angles and sides between these triangles. By using CPCTC, we confirm the congruence of corresponding parts of the triangles.
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Answered by etumnulemuel | 2025-07-03

When triangle FGH is the image of isosceles triangle FEH (with ) after a reflection across line HF, then triangle FGH ≅ triangle FEH, because reflections produce congruent figures.
Now, by the rule of Corresponding Parts of Congruent Triangles are Congruent (CPCTC), we can say that:

✅ The following statements are true:
1.
(Corresponding angles in congruent triangles)
2.
(Corresponding sides: FG ↔ HE)
3.
(Corresponding sides: GH ↔ FE)
4.
(Corresponding angles: GFH ↔ HFE)

Summary:
All statements about matching angles or sides in triangle FGH and triangle FEH being congruent are valid due to CPCTC, as long as they match the original triangle's parts in position.
Let me know if you'd like this visualized with a diagram! ;

Answered by etumnulemuel | 2025-07-03