Question

triangle fgh is the image of isosceles triangle feh after a reflection across line hf. indicate whether each statement is a result of corresponding parts of congruent triangles being congruent. fe ≅ he a. efgh is a rectangle. b. efgh has four congruent sides. c. diagonal fh bisects angles efg and ehg. d. diagonal fh is perpendicular to side fe. e. angle feh is congruent to angle fgh.

Explanation:

Step1: Analyze option A

For a quadrilateral to be a rectangle, all angles must be \(90^{\circ}\). There is no information from congruent triangles to suggest this.

Step2: Analyze option B

Since \(\triangle FGH\) is the reflection of \(\triangle FEH\) and \(FE\cong HE\), by reflection \(FE = HE=FG = HG\). So, \(EFGH\) has four congruent sides.

Step3: Analyze option C

Because of the reflection (which implies \(\triangle FEH\cong\triangle FGH\)), the angles formed by the diagonal \(FH\) with \(EF, FG\) and \(EH, HG\) are congruent. So, \(FH\) bisects \(\angle EFG\) and \(\angle EHG\).

Step4: Analyze option D

Let \(M\) be the intersection of \(FH\) and \(FE\) (by reflection properties). Since \(\triangle FEH\cong\triangle FGH\), the angles formed at the intersection of \(FH\) and \(FE\) (corresponding angles in congruent triangles) can be shown to be \(90^{\circ}\) (using properties of reflection and congruent triangles).

Step5: Analyze option E

\(\angle FEH\) and \(\angle FGH\) are not corresponding angles of congruent triangles. Corresponding angles of \(\triangle FEH\) and \(\triangle FGH\) are \(\angle FEH\) and \(\angle FGH\) are not in a corresponding - part relationship.

Answer:

A. Is NOT a result
B. Is a result
C. Is a result
D. Is a result
E. Is NOT a result